to the Insan Literature Group of Virusine Chat. The Virusine Chat is a program of the Literature Archives in the state of Chicago. I'm Doug O'Keefe, a host and producer of the chats. Today, my guest is Margaret Graff of Tronson, Norway. And me, Arlene, Tronson, will be the very first Virusine Chats above the Arctic Circle. So, now Arlene, what are your feelings of being the first Norwegian Virusine Chats above the Arctic Circle?   Thank you. Now, what do you think is unique about Norway to church? I think that we're kind of, kind of in the world of including animal in the church. We believe in the rosary, we believe in the blood. Before we get too far, we're going to very, very important speak to you, this church. Please tell us about this church here at Tronson. This is what we innovation call Tronson Longing Gap. It's the main church in the city. Now, it is approximately 150 years old, of this style. I've been taking seven years, and I don't do that anymore. But my parents, they do things and needs with the church and the world of doing it for everyone. We are all here. What work did you do here? I was working in the children's youth and the rainbow boss, the stories from rainbow stories. Education. There are some plans to use the services here that are very important to the life of the church. Yeah, tomorrow we will have a service. I'm in Bishop, living with the very first time of joy. I'm here to look at his speech. I'm here also to participate in the communion, which is a very important single for the church. Why so? Because we think that we're on the right way. Thus, here, everyone is going just to be a human being. When we were preparing for this ceremony, you told me a little about your growing up in your family. Please explain that for me, Alice. I grew up in a little village called Voldemort. It's a place in the northern part of Norway, and the song you're going to show is really strong back now, but for several years it was addressed. They wrote the love, speaking the language, they're doing the singing of songs, they're doing the burning calories. Children were taken from families and sent to the end of their boarding school when they had to leave. They were forbidden to talk the song language. Instead, they lived with the people in Norway. And of course, very climatic, filled with both shame, shame of being cruelly in the bar, who you want to be. And it's almost like when someone is drowning and trying to help them, the process is kind of gross, evil, but if it doesn't make its worth it, and now there's nothing else, it's really growing and getting so much stronger. I had to... Ah. Yeah. Please explain for me the international life is a little more out of some culture. I think many people don't know. I think you can count on compared to the native Americans that believing that the earth is holy, the name is kind of a God, the water, the earth, that the earth is divine and that we should treat it with deep respect. And the music was very deep, using that, you know, from just like a native American. Now, has this process of taking your children to know this whole song? Yeah, this song, I think, may 60, maybe a little later. Now, the Song culture is very unique to Norway. Where exactly did someone find you in the cities? Actually everywhere in Norway, because some of us still feel deep in shape about being something. And I think you can count on compared to being the group, you do have the risk of being called one, to get the next, it's it's love, things like that. Just hoping to do the best things in terms of such a night. You were 14 years old. You created this study. Tell us about that. Yeah, I was getting really good at school. So instead of just being paralyzed and doing nothing, I said to myself, but back then we had to do something to create a meaning of being here. And then the whole world, this is back in the 80s, and okay, why not? What are these? So I created this number one piece, and we were thinking of politics, history, what to do, just looking at it so helpless. How many people were part of this group? 80 to 10, I mean. This was a really small place. 800 people together in my class were 16, and they were joined by students from three other schools and then they left every two of us. What sorts of things did you do? In a certain group of students, we were really used to having a very open body, getting used to keeping up to date with the news. And this was many many years before this social media had a new social cluster, and once I got to it, if I hadn't been in, right, down, so we didn't make work, they would have sent in a lot, and maybe it was really what I'd taken, and I guess we did, but not necessarily to the news people and the people. What particular topics during the Cold War were you most? The risk of the atomic bomb, and I just knew before that the whole part of what I did was just being erased as a picture of what I was doing and what I was writing, standing in gasoline, up to the whole day, and I was like, wow.  I really love you. I believe in the power of the Buddha. It's kind of good to believe that people are good. It's a change during the end of the day, because I really like optimism, and I do need to change. And I love the stories. Who don't see what they do, was the motivation for their decision to make. And since I arrived to the world, when people are curious, really need knowledge, what would be a better job than being a teacher? I wouldn't imagine that. What sort of motivation is that? That a change is possible if you do acknowledge people, people and their way of experiencing the world. I can say that's wrong, but I can say that I hear you, I see you, and I do understand that this is either difficult, or important, or difficult or general, clearly between you. And then I ask what would you say? What has happened in your thesis? The paper marks this as an example because a lot of people I know in the queer community have so many bad experiences in the Jewish community. There's been a lot of talk about sin, shame, right-wing in arms, and hell. This is so far from the God I'm completely being. So I said to you, at least we do have to do something, because it's still and doesn't do anything about this. It can really mean that God is the creator of everything and the world. We have to shut it. The community today, there's a very big push for my thesis, who are women in the community. How do you, my head start in the community? That's a very big push there. I know who lost, but they gave me a lot of money and then of course I don't want to be to cry because the heaven and me are queer. Yeah. And I'm proud. And I do cry to be a preacher because I do believe that we're stronger together. We don't have to believe exactly the same things, but seeking was common. Seeking share is more important to me than looking for the differences. What does queer need to do? Something else than a square, that's the kind of form. Yeah. No. It doesn't matter to me. Really, it doesn't matter to me. Plus I'm difficult somewhere but no, it doesn't matter to me... What about... What person are who you are for 2 to 2 It's much smaller than the generation identify with, what we should say like this. You do it like this, okay, God is so much more than we can imagine that He's really trying to label God. God is divine, power, love, man who holds God. That's it. I'm trying to find a way for you to explain to us why we don't automatically go with the traditional. You can explain a little bit about that, but I think many people are a little confused. I don't think I told you this in the first time. It's better in the same way as you would have explained. And I don't know what to make. In the script it said the mayor was to be a man. You appeal all of the subjects really, really important. And as he gave it to us, I said, no, I want to be a man, and the other has to be a man. And so it's allowed us to have amazing voices, evil, fissure, man. Everything is allowed to be a man. So I don't know why. But I want to say that we strain people from being free, out of time and what you feel, using the knowledge and talents, very well. Me, the animal, and not being afraid of being a judge, learn how to take everything with the legs of Sue Smith. How do the audience react to that? They were really surprised because, of course, this was in our preview. So they had a better play. And so everything, and when they came upon the show, everything was allowed to be a man. Was it possible? Yeah, it was possible to be a man. I think it was a lot of services. Okay. But as I said in your show, you speak a lot about your religious faith. What so strongly draws you to more or less Christian ideology? Because I have to wonder why that versus Islam or Judaism, for example. I think, of course, my parents have a lot to do with it because both of them are Christian. And also in the community, I grew up with a very religious faith. And as well, we were not allowed to sing and do the same talk. But of course, there was a dance and singing. There was dance in the need to sing. Which is called singing itself. And when we were having a religious space, music worked a lot. And when we were supposed to learn about unaccepted, stupid, and separate manly parents who just grew together with the nations, so that their kids were able to see it. And of course, being a parable, I was trying to figure out what else is there on the topics. And my parents took me to some camp. We're a local priest from South Africa. And we're very close to national values. And I couldn't speak German. I think we also have a lot of very good German faith. You see that I am a student twice. And they were both Christian and rebels. And really, what else? Some of the human rights. And I thought, oh, that's my culture. And later on, I got a lot about feminist theology. We had a liberation theology in Latin America and the Holocaust, yeah? Yes. So, non-theology is about slow and non-serial. And not it's not justice. Not through votes. That's legal principles. We're pushing. So you can see that differently in the teachings of one. As I know them, yes. But at the same time, we do know that there are feminist teachings. Yeah. Yeah, there are changes. Both in Judaism and Christianity. It's not a liberal. The world is changing, but it takes time. There's something you think is a little separate from Christianity. Jesus himself was a rebel. He was actually a Jew. And I said, no, I'm a Christian. No, actually. So he was a revolutionary. And he saved the pros and cons. He saved the saviours, the peace, whatever. Yeah. I'm just trying to understand the difference between these so that it's clearer. I found your conviction to be very fascinating. Very powerful. So I'm trying to understand a little more. I think maybe you can compare it to our relationship. You will need a both interrelationship because it is sensible. Or you can be giving my up to be a model of faith. But my Christianity is pure love. It's not because it's so small. It's not just a favor. Even though for many years, I couldn't believe God had born because of that son of a Christian. It's too late. So many bad things to me are to reach out to other people, traction and blame in them. Just thinking about seeing their name in the heart of their being instead of being a model of God. And maybe go like this into the world. But that's not the way it is at all. That's a good judgment. It's all about love and aggression. Wow. I'm going back. I have a great question here to say. Are you made up for human faults? Yeah. I have done that. I will be the image. I'm really afraid. I'm not good. As we have been speaking this evening and actually about it, it's like when we prepared for this interview, you see people as walking energies, including something divine. Please explain that for us. Yeah. Nothing can come out of nothing. And when I die, my energy will disappear. My problem turning into the growth of ashes of the lotuses and my energy will not go away. It will take a long time. And if I do believe that I am walking energy, rushing to grandma in New York, and I do believe that nothing can come out of nothing, then there is something more. And that is really both fascinating and highly frightening even though I've lost a place because it makes it clear to me that there is something bigger than me. And I can feel it when I'm outside getting the grip in my face, the wall coming out from that sky. I can feel it when I'm touching the growth snow, feeling the struggle out on my face. What we need to be oxygenated and not being wasted. These are holy words. And when I do see you, and I see the growth in you, I see that you are. Because we are all created to be equal. Does it make sense? I'm not going to be sure. I just see it. And I completely understand what you seem to feel, what exactly it is. The first time I saw you was when you were a small man who was heartily covered in tears. I still feel a lot inside you.  It's very, very different. You open. You begin with this. I felt the curiosity that accept us. And those are positive emotions growing. I end. I'm not labeled as something grossly, even though I've seen many people on the earth. I feel if you're open to the energy of love, then you're a child of it. If you're not open to it, if you're not gay to it, you need to challenge it. Thank you. This is an artwork in which you smoke my legs and talk. Thank you. If you're not able to feel in love, you can't shambles it, or you can't express it, and if you need a thumbs up, show that all people are in love with God's divine. Very good. But also when we were preparing for this, and you mentioned this a few months ago, you said the institution of the church, however you define that, has alienated the distance and harmed people driving away from this church. How would the church do this? With the two speaking, that sex, sex, marriage is the same, homosexuality is the same. You don't speak a lot about fetish. You can do other stuff, and you can do everything in which other sex is the same. So everybody wants to have one more, another, one more fetish. We would feel ashamed if we do pay attention and listen. And they have said this for so many years, and not only that it's the same, but you do a lot of things you want to have, and you want to both have the way they describe it. No, no. So, people have been judged, labeled, and of course, we must be together and someone is going to have that kind of requires a lot of good life there. It seems to be one of those that's going to have no harm. So of course, I mean a lot of fear, a lot of fighting, a lot of shame, a lot of anger of change in church when we're in it. So I think it's kind of easier to turn our back against the church and just walk away to face it at least. So, there have been a change. There have been a change. But if that's how we get into the room within the church, it's like I'm happy to see you. I've been fine. Yeah, I think it's going to be easier because it's sort of being in a struggle not quite all the time, and this is what it's all about. You want the church to take place and you change. And the church have now decided in their way that we do the same-sex marriage. In this church, open a man and then we come back home in their being. Some priests say, I don't agree with this, and they don't have to do the ceremony. It's really an involuntary church. Even though it's kind of tough in the north, it's tough in the south, but it's a change here. And that's why it's so important that the vision will be as a service to all. Because it's a heritage. How do you see the church in a bigger picture? On the roof. On the roof? Yeah. There are still a long way to go, especially if you've got a gender identity. We still use E and She for the most. And I think we're going to need to go as men as their child. I think that the forwarder will be more interstitial than just mother and father. And we need to move as we say in the vision, and move a woman, mother, father, father, second, second order. This is not the forwarder being filled out. And we need to find that Ramadhar. I'm not going to talk about the vision. Ramadhar. I think it's heresy. Oh, heresy. Yeah. Heresy. Yes. Maybe there is two mothers and a father will be included. Are you the same as? Do you still see that people should just have their children back at us? No. It's the same but really it's emotional because I think that the church too has an important role. It's very important in the church. We do need to have some place to go when life comes. It's either in a good way or in a difficult way. And in the church the people who work there are still the many people where they are. We are alive. We are emotional. Why do you think people are doing that? Because all the men celebrate the new life. And in all ways the moment has celebrated the name of the new being. Yes. And they put the products instead of talking to the church. And all in all ways the more there are secular numbers much like that. And we see it also in that individual information of the ten years old that a lot of people are going for a job. The moment is which is secular information instead. Yeah. Okay. I think you kind of should be about to give the the rest of the time as an artist and meetings because I'm the mother there. Yes. And to the same church because I also belong here and as a need to talk we need to meet a human being in Cyprus. That's why we have this. And outside the church tomorrow we will buy some time and it will be there until the service tomorrow arrives is finished. When I make the church I have this waiting for the dawn through the afternoon. Down the island. Yeah, meeting people can not come here much. We use people in here for the service. It's visible up here. We don't deny anyone to join the church. And I do collaborate with communities and it's so important to have a place to meet. Being clear with God can be very hard. Maybe we don't have the language for who we are maybe we don't know anyone else but we make this place where we start with us before that and then we open some of that they don't need to know anyone but then they have someone to call together with the place. And I also says that we need the social part so we go without the place. But once opened people do notice people do listen to people. And they don't have experiences that make them believe. Maybe they have told things that they don't know and they don't have experiences that make them believe. Maybe they have told things that they don't believe that they just have to accept this and be a Christian in my way and maybe they can see that there are authorities. It is possible to be Christian in many different ways. Maybe they can find something to recognize really powerful. Very fascinating. I have been very very curious about our sort of ministry with the LGBTQ youth. How have you achieved that level of success? How have you young people respond to you? If you really might have such new assets they're not afraid they want to. They can be a place for whatever if they want to they take over them they can possibly whatever and never come. And they thank a lot for that very excellent service and love which also must I wouldn't talk because of the community. And unless some of them when they were only 14 years old and of course it's generated new people that say I've grown up and since I kind of succeeded in the first time I was there I don't know the recognition yet. But who do your parents respond to you for example? I've had several phone calls and he answered with me when I met them Thank you for being there as an adult you do feel safe spend your time with your daughter or whatever they label it to your arrangements Thank you for creating this community my child must not feel that alone my child don't feel that at all anywhere and more and that gives me really more motivation because I remember this feeling on the other hand anywhere it's horrible it's horrible it feels so alone so afraid depressed sad it takes so much energy to go home try to think of you to be together with and if you do fall out at your age it's so hard to get back into society to get education to get work to get family to get relations to reach out to people who must do all of them they're so important Good question My mother started to be when I was there most people have a school TV on the channel on their heads you know the old television was like you have a wolf and it's huge so I kind of sense it people do need to talk to me want to talk to me are curious about whatever it's for you today and if you want they can bring up topics talk about and if you don't want you don't dare maybe or something I can imagine young people in a small town somewhere I just don't know where they're from you know if you're in a remote village for example I believe you fall in love with us I'm really used to peoples but ever I have the opportunity to stay for some day about some inclusion and diversity I try to do it even though in Tokyo Tokyo are open and on Tuesday we do have some surrounding questions we use every opportunity to stay and still say I shouldn't you don't you can't do and if possible I need to argue with them if possible I answer them in the paper what's going to be it's about on this full page in the paper with me with this handle bring your colors on my head I'm angry against a priest who has been divorced three times right the wife says a lot of lot getting divorced but he married he does not say a lot of lot since his marriage but he was wishing against the same expression why I didn't know to me but I did want to be with this were you successful thanks I'm not your thanks thank you you're good you're good now in a very broad sense your work is sort of like a mystery how do you combine your work and your mystery with the work that's going on which is our post event this weekend I remember when I reached out to our group I said we would like to have stories and make more stories with your life to be a core a role model is amazing yes it was not necessarily expected because since the church has done so much wrong and said so many horrible judging things even though I reached out to my house be sure that the other people would say yeah we want to jump but we did and we went to a lot more arrangements and talked with the community here and we engaged in whatever catches my interest and of course making a license is not something that happens or at all you have to put energy into having it you guys what's your question it seems a bit of a bit more than going on because it's a very interesting mixture and I wonder how you succeeded to do it being honest being honest and sincere and of course try to remember and of course I'm not in a position that I can judge other people I don't know they don't know what to do so I'm just wondering yeah I'm going to have fun I'm going to have love I'm going to have nutrition and diversity I want the whole world to be as more available that's my question you were first this combination yeah yeah it's so powerful it's so powerful and the message from our pride is diversity it's love and and it's the same for me and I two possibly both together makes it even more possibly even stronger that's fantastic you're absolutely beautiful but what do you like the international community to do about Trumpson Arthur Cronin your work and their work you're always welcome in Fulsa but every time in Fulsa you are welcome you could reach me on Facebook the church is made not open during the day but there the page is coming up in faith in challenge or temple whatever the divine has created each and every one of us don't be afraid to challenge them do you think God or the divine may mistake creating me I'm sure the divine has a special way a special moment now what do you feel is the business misconception of the shirt that people tend to have that he has changed that we still the old dark times when they were very anxious and no we know that no more they have really a lot of change and please give us a chance you mentioned that I'm going to send back for a second but you mentioned Arthur Cronin he used in the Lord products some words about that last year I got this prize for being yeah an activist yeah for all my work throughout the years living inclusion of diversity bringing people together and reaching between the church and the community I was really honored and totally open relevant and surprised how long have you been and the national level thus far it is almost beautiful since 2008 when actually how how so I remember the National War this week which is say this must be this that it is and it has really been normal okay so what is the business in such a way people have about normal that I swear so I'm walking to follow the twist it's dark all the time or the women started shining all the time because about a minute I have to tell a little story yes it has some tourists okay and wanting to see the video of someone and the guy said I don't know who I am get me a video it's just the same son but it was not going through the price of the below the price stay low so they were very disappointed you can choose who is the first coming to normally to see the war but during the summer that is so many minutes so please read from the circle of the area for your tickets this this time you are really the daylight few hours of the day time yes half for one and a half week we love the horizon stay if you want to now what is the previous conception about you I am an explorer especially very very sharp people usually don't very happy to stay long in my decay so why don't you it's impossible to make a change you must stay there but at the same time I do not people I do not interact with people I am not making things together for me exactly and yeah this is my this I am so pleased that I hope it suggests you for your dream this has been absolutely wonderful I am very honored to be suggested and accepted it's my pleasure so I would like to thank you for this amazing interview from inside of my history the fireside chat at Archer Cry in Charleston thank you so much for both of these events in this church thank you so much for me this is very important to hold it here in the church does that please yes just look how do you deal with people's anger how do you deal with people's anger don't imagine I have this hook of thoughts about you for us yeah I am very conscious about where do I stop and the other are cooking and now I can still be very close to very angry people keeping my breath dark in my belly is number one stretching my back is number two and then I hear what he was saying difficult to meet I was down in the shops can you please please try again in the open box and then I will try to come up and move her back upstairs I understand a little bit who you are I'm wondering did I understand what you're saying creative it's over yes it's not right it's not so people don't stay everywhere at all if you might go to an average car if your face is open and my eyes won't junction usually the anger kind of lasts away very good very good but of course I don't have to read them I can say I hear them say and I accept that and I do expect your voice to rather appear here or experience but on the other hand my experience my belief are human but if you come up against that kind of really absolute angry person how do you stop yourself not getting angry against that reaction no it's not here I don't know how do you react strongly believe that everyone has every time is doing their best and when I do believe that everyone every time is doing their best of course maybe another time can do much better but I'm giving something inside of me that it makes you feel kind of helpless you don't get very angry you feel empowered so if I try to find the empathy it's much easier not to get driven into their emotions the same you know yeah good idea thank you another question for me I don't have a question but I have an observation if I may observation you sure so you know you say with angry people you have this forcing around you a force like yeah you know you are one of the most open people I have ever met one of the most something kind giving understanding I mean so many different words I could use to describe you kind of you understand okay you're a people manager thank you people who tend to gravitate towards you because they can see this openness and this love and it's what to make them open this love sure openness it's true it's so true I speak only the truth I'm in the hands of God and I speak only the truth why do you think we rushed so much just together we checked in the hotel and just left everything that came here okay we don't even know yes for the audience we watched this video the whole I wish you the first time that we arrived here I think it was 2018 and Marie-Mathé you made us feel so welcome so part of what was going on in a small city within the Arctic Circle and we had traveled so far to just experience this and you only enhanced our whole experience here by just being who you are a beautiful city I mean you've enhanced so much forever we are really attached of course and just each other saying hello I'm so happy to see you it was really coming from the heart we know it and we can feel it okay thank you everyone it's been a pleasure


What's up everybody, it's Stas here and in this video I'm going to be sharing with you all three stocks that I'm looking to swing trade right now in the month of October, heading into the month of November in 2019. And when you're swing trading in the stock market, the key is to buy low and to sell high if you're looking to buy actual shares. If you're looking to short a stock, maybe swing trade put options, that's a completely different philosophy. We're strictly talking about buying and holding shares here, which again, I'm personally looking to buy at a dip and then really sell as the stock continues the uptrend and breaks out. And all I ask from you guys is if you enjoy the video, feel free to go down below and hit that like button and consider subscribing if you do want to see further content about the stock market, both investing and trading. And feel free to join our free Discord group chat and our free Facebook group, both of those are linked down below. So as you can tell, the first stock that I'm looking to swing trade here is ticker symbol T, also known as AT&T. And a quick disclaimer guys, don't just buy these based off of my opinion. You have to do your own research, understand the risk involved with these stocks and understand whether or not it fits your personal criteria and your philosophy when it comes to trading in the stock market. And also, all of these companies that I'm going to be talking about in this video are reporting earnings and that's also a big thing to keep an eye out for. Me personally, I don't like buying stocks before earnings. I like getting in and out before earnings and buying after, right? And that's kind of what I'm looking to do with a lot of these stocks. But just keep that in mind because earnings, guidance, the numbers they actually report in terms of their earnings report, these companies that is, right? This can heavily fluctuate whether the stock is going to go up or whether or not it's going to go down, right? It fluctuates the stock. So AT&T here, they report earnings on the 28th of this month. So that's in 10 days. So we do have time to hop in and out here of AT&T before these earnings, especially with what I'm seeing here on these technicals. And let me break it down for you guys, right? I said a couple of minutes ago, the key when swing trading is buying low and selling high after the stock continues the breakout or as it's breaking out, right? And right now we're seeing AT&T is doing just that, just that, right? And that is, it's breaking out. You can see here $38 is a clear resistance, roughly $38.90 up to around $38 bucks here on AT&T, right? We topped out here once, twice, three times, four times, five times. We were struggling there this morning. But now that we're breaking out of that resistance, that's extremely bullish. And I'm thinking that AT&T is now going to push to fill the gap up here to $39.50 to around $40 bucks. And how did I get that $49.50, $40 bucks level? Well, if we zoom out a bit here, let's go to the three-year one-week chart. You guys can see actually that we've been rejected three separate times at around that $39.50-ish level back in 2017, heading into the year of 2018. So that makes this level a very strong resistance. So all in all, at this point, guys, AT&T, to put it in brief terms, it's breaking above $38, which is very, very bullish. And now it's looking to fill the gap up to $39.50. And another important thing to keep in mind when swing trading is how much risk is involved and how much reward is involved with particular trades. Well, in this one, from $38 up to the resistance where we would ideally sell, that's about a 3% profit margin. And where I would probably cut losses on AT&T is if it were to break below $38. So from where it is right now, down to about $38, that's around a .5 to a .6 risk in terms of how much you can lose on your position. So about a .5, .6% risk versus a 3% to 4% reward, that is pretty good in my personal opinion. So AT&T is the first one that I'm watching. Ideally, I'd sell up here. If we even break above that, that would be probably a sign to hold it even up to these high levels at about $40, which at this point would offer even more margin right from down here where we are now up to $40, $41. That's going to be around 6%. So just keep an eye on these guys. AT&T is looking very, very good. Just keep an eye on these levels and the technicals that I'm talking about here. The second stock is going to be ABV, ticker symbol ABBV. And this is actually looking very similar to AT&T. We're breaking above a resistance and we're entering into a new channel where from where we are now at about $76, $77, up to the resistance of this channel, that's about a 6.25% profit margin. And mind you, just like AT&T, ABV is reporting earnings here in the next couple of days. I think they're on the 1st of November, so they actually have a bit more time than AT&T. So the idea here, the goal here would be to maybe swing trade this, get out before earnings, see what earnings does, numbers, guidance, all that good stuff. Then maybe enter back in if the earnings are good, if their earnings are good, if the guidance is good, and if the stock is positively reacting to those earnings, which is very important. But as of now, we're breaking a critical level. This is a level where we kind of triple bottomed here a couple of months ago back in April to May into June of 2019. And once we broke that triple bottom, that made this level a strong resistance. We tried to rally back up a couple months ago back in July. We ended up failing, ran all the way down to about 62 bucks. We tried to pop up and test that same 76 buck level on the 1st of October, failed again. And now we tested it yet again yesterday heading into today, right? And now we're getting the breakout, which just like AT&T is extremely bullish here on Abvy. So risk reward, about 6%, we saw that to the upside, to the downside here, about 0.7% to around 1%, right? And typically, I'm looking to cut losses whenever my swing trades break critical resistances. And honestly, whenever they get below really 1.5% in the red or lower, because that's where I'm typically keeping my stop loss when I am swing trading. And when I'm up on a position, I'm typically keeping a trailing stop loss to protect those profits. So let's say if I'm up 5%, 6%, I don't have a trailing stop loss. I'd probably get wiped out if this were to dump. But if I had a trailing stop loss, I was up 5%, 6%. And let's say the trailing stop loss was set at like half a percent or something, then this falls half a percent. Obviously, it would sell my position and I would lock in those profits. So that's really just a mechanism of protecting your profits. And again, that's what I would do if I was in at this point, or not really in at this point, if I was seeing a good amount of profits at this point, right? That's what I would do. So Abvy, that's what I'm looking at. It's in a new channel looking very, very good right now. Very swing tradeable in my opinion. And the last one, which is another one that I've been talking about a lot on the channel, is Procter and Gamble ticker symbol PG. And if we're just looking at Procter and Gamble here on the 4-hour chart, it's clear that it's on an uptrend, right? And it's clear also that we broke that main support level, which was the 180SMA that was holding this uptrend intact. So ever since we've fallen beneath that, you know, Procter and Gamble has been a bit bearish. We're seeing the moving averages acting as resistances rather than support levels, right? We're seeing a bearish cross here, the 50SMA crossing below the 180SMA. And we really haven't seen any upside push here until now, right? Now we're starting to see some support at around 116, 117. And we're starting to see a bit of a breakout here to the upside. You can maybe say this is a double bottom, triple bottom. If you're counting this one, twice, and then three times today, now that we're breaking up. You know, I guess that could be a triple bottom here. But overall, guys, the trend is looking like it's slowly starting to push up. Obviously, we have earnings here, and really, actually, I think this is the soonest out of the three. Yeah, it's on the 22nd of October, so this can heavily fluctuate the stock up or down. So for me on PG at this point, I'm probably going to wait until after earnings, since earnings will be, I'm guessing, on Tuesday, which is the 22nd. So I'm going to wait until after that, see what they report, see how guidance is, EPS revenue, all that good stuff. But either way, I think this one's going to offer some good margin, right? Okay, 118, if we enter it hypothetically here, up to around 125, that's about a 5-6% margin of profit. And I would definitely break or cut losses if this were to break 116, because this is just a critical level of support, guys, right? It was an old resistance. It was a support back in August as well. You know, it's just a very, very strong key level. And if we were to break there, that's where I'd cut. And from where we are now, down to about 116, that's about a .6, .7 potential downside here in terms of the risk. So the reward heavily outweighs the risk right now in Procter and Gamble. And if we zoom out a bit, let's say to the three-year one-week chart, what I noticed is maybe let's go to the one-year one-day better. Yep, this is better. What I noticed is if I draw this little uptrend here, guys, you can see that this is a bounce point for Procter and Gamble on this one-year one-day chart. So that is interesting if you guys do look at these long, long-term charts. Well, not extremely long, but longer than the usual timeframes that I talk about on this channel. This is definitely pretty interesting in my opinion, right? We could end up holding this and popping, you know, if these earnings are good especially. So overall, guys, those are three stocks that I'm looking to swing trade right now in October heading into November. And again, don't just buy these. Don't just swing trade these based off of my opinion. You have to understand that they're reporting earnings. You have to understand these earnings and these companies for yourself before swing trading them. Because let's be honest, the whole idea is to become a self-sufficient trader and investor in the stock market. You don't want to have to go to the internet to really see other people's opinions before forming your own. You have to have the tools to form your own first. And then, sure, go on YouTube, go on the internet, see what other people are thinking, and then that's how you can collaborate. And then maybe build on your own skill set with other people's skills that you get from really just looking at what they're doing and kind of adapting what they're doing in a way, right? So that's super, super important. And other than that, that's pretty much it for this video. If you enjoy the video, feel free to go down below, hit that like button. Consider subscribing if you do want to see further content about the stock market, investing, trading, and personal finance. And also, don't forget to join our StriveSmart Discord group chat and our StriveSmart Facebook group. All of those are linked down below as well as my Instagram. So I'll catch you all in the next video. Thanks again for watching. Have a great weekend. Peace out.


What's going on guys and gals? Brad here for late in sports cards. We're ripping first break of the night NC basketball, prism basketball, two box mixer number five, random teams. Here's that list one more time find that on the results tab of the website at any time and of course thank you for joining. Let's see what's going on here guys. Purple, Aaron Gordon. Oh Jesus camera. We got Jason Tatum insert. G1 Suggs. Rookie. I can see Clyde Jones. The camera can see me but I can't see the... Yeah they can see you. If they can see me I just can't see myself it's all good. Silver Keon Johnson. Clippers Rookie and a Hyper. Marcus Morris senior. Wasn't there that conspiracy that they swapped places in the finals? Josh Giddy. There you go. Base rookie. Because they have the same tattoos as well. So like it makes it easy. Red Wave by Zea Roby. Red Bill Russell. Celtics. Chris Paul. Juan Toscano. And Kessler Edwards. I don't know if I'm supposed to be handing you everything. Uh some of them are probably on my wall. Okay. Ty Drum Silver. Blue Gary Trent Jr. 75 years. Devin Booker. Got a Josh Christopher. And Herbert Jones. I was zoomed in. I knew something was off dude. This is not effort to be on the wall. Got Red Wave Yokech. That's it. Do you have what the red jersey? Yeah. It's pretty. Got G. Some Williams. No not number. Conlon Tim Duncan. Duarte. There you go. Sam Hosslin. Silver Royce O'Neill. Kawai Leonard. I haven't broke with a top litter in a long time. Quentin Grimes. Bones Hyland. Front Rookie. Austin Reeves. What is this? I like those. Oh Mojo. Mojo of those. To 25. Prismatic Paul George Mojo. That's sweet. Those are cool looking with the rainbow with the Mojo layer. Wow. That's sick. Hey I'm sorry Minnesota. I just saw you. How you doing man? This is not first off the line. I got Cabs. Silver Rookie Otto Evan Mobley. There you go. Nice man. That's awesome. Nice Silver Rookie. Sensational Sigs. That's a nice signature too. Got Brandon Boston. Corey Kisbert. Nada. Albrin Shangoon. Silver Rookie. Hyper Eric Gordon. Cabin Durant. Evan Mobley. And Tray Man. Where are you at this one? I was just at this one because they had all of those for the prismatic. Yeah it's gold. They have Mojo and 101. Roy Hachimura. Not numbered. Red DeMar DeRozan. 299. Luca Garza. Wilt the Stil. Namious Kata. Wilt the Stil. Oh yeah. Oh yeah. When I met Karim it was the same way. Austin Reeves. Silver Rookie. Purple Ice. Jalen Noel. There you go to 149. Scotty Lewis. Aaron Wiggins. Did you go to that national? No, Soldier Field. No. That's where I met Karim and Tyson. Got Red Wave. Deeron Sharp. Rookie. Hyper Bobby Portis. Beast Beast. Charles Bassey. What's up Double T? What's up Ryan? Thank you. Mo Bamba Silver. LeBron James. Fearless Silver. And Jazz. Otto Ersan Ilyasova. Rookie Keon. And Rookie Jaden Springer. And my first NT. Let's do it. See ya Kenzie. Always Texture. Can always Messenger. Oh yeah. Not there yet. I had to scare it once. To 99. Demona Sabinus. Kings. Why does forest happen? Maybe. Printing Plate 101. Colin Sexton. That is in last year's NT. Next Seawolves Jersey. Jamal Crawford. Dude Rich couldn't say this name for a while. To 99. He would say Jamal Crawford. Or something like that. Or no that was Jamal Charles. I'm sorry. Jamal Charles. We got Patch Wizards to 25. Rui Hachimura. I'm gonna pull a Logan man. Jamal Charles. Yeah I mixed it up. That's my bad. Celtics Auto. Kevin Garnett. 14 of 49. Celtics. KG. RPA. Quentin Grimes. To 49. Mix. Look at that Patch. Four colors.  This year's NT Patches might be the best I've seen on The Truths. Wizards Jersey. It's Kyle Kuzma to 99. Kuzma. We got Cavaliers Jersey. Jared Allen to 99. Devin Vasell. Spurs Auto to 99. Guy 16 left for the next Prism and NT 2 Boxer after this. And Nugs. Jalen Rose. Auto 29 of 49. Nice Rose. Guy who gave up 81 to Kobe. And there you go. Let's go through these real fast. Alright we got Jalen Rose. Jared Allen. Kyle Kuzma. Rui Hachimura. Jamal Crawford. Devin Vasell. We got Evan Mobley's Silver Rookie Auto. Which was nice from Prism. We had the Kevin Garnett to 49. And the Quentin Grimes. RPA. Four color Patch to 49. And there you go. That'll do it for the hits. That'll do it for the break. Coming up next. Same type of break. Let's get it.


Now, we are going to state a relation which is kind of going to combine what is the next going state I am going to take given that I have already spent this much of time I have already spent in my given state right. So, this is already what is the state you are just going to state j whenever the jump has happened when you started from x not from state I, but you may also ask the questions like on this state I have already been there I have already spent this much of time and after this what is the probability that I go to state j ok. Let us formalize that I am going to ask this question now. So, what we are asking is here suppose you have been given that the jumps have happened at time t 0 t 1 all the way up to nth jump and you have been told what are the states that has been taken when this jumps have happened that is x 0 corresponds to the state at time t 0 and x n corresponds to the state at time t n of your continuous time Markov chain ok. You understand the meaning of conditioning like this. So, basically saying that these are the instances at which my jump is happening and these are the corresponding state that has been taken when the jumps have happened. And now we are saying ok fine it looks like so far n jumps have happened and after that you are asking the question before the next jump happens that is t n plus 1 it is going to take at least u units of time and after that that the jump I am going to make is to a state j and now what it is saying that this probability is nothing but the probability that you are going to stay in that state this is a to the power a i u right that is what we have shown and then from that state the probability of going to p i j. So, in a way what you are saying is see when I define p i j I defined it for one full life cycle right like t 1 before this is for all t 1, but here you are further asking this question that before you starting from this state i when the n jump happened you are going to state j after spending at least this much of time it is saying that then if you want that extra conditioning that not only I want to go from i to j, but I also want to ensure that before going to state j I am going to spend at least u units of time then multiply by that probability and in a way it is saying that this is a design that these two are independent right because it is just multiplying both of them ok. So, let us quickly write down couple of steps in this proof probability that t n minus n plus 1 minus t n being larger than u x n plus 1 plus j given. So, first thing it is a CTMC continuous time Markov chain. So, already know that it is going to satisfy Markov property. So, once I know the nth jump is going to happen at this time I do not need to know any of the things which is happened before to answer question about my feature. So, this is about the future after nth event has happened right I am going this is about that. So, to answer this question I do not need to know what has happened before the nth jump. So, I am just going to condition it on this event that t n is some number which is given to me that is a random quantity. So, basically this is exactly ok this is nothing, but x n in our notation x n we have defined x n to be x of t n. Now, I am going to use my strong Markov property let us say and then also nothing not strong Markov, but just now let us say I am going to use my time homogeneity property if I can use it. Then yeah along with my strong Markov property I can shift whatever happened at t nth instance as it has happened at origin and I can start looking from that point onwards right. So, t n I can assume it to happen at the 0th time in that case I could write it as now t 1 greater than u q 1 x 1 equals to j q 1 x 0 equals to i. So, now everything this Markov chain I will just shift it to origin and now from the origin I am asking this. So, I am basically saying ok at the beginning I am in state i. Now, I want to t 1 I should before I jump to next state I should have spent at least time u and my next state should be j. This one I am going to write a probability that t 1 greater than u q 1 x 0 equals to i probability that. So, I have just applied my chain rule here and I could write like this. Now, what is this quantity here?  What is this probability? e to the power a i u that is the definition we have right. So, good we already have this term. So, now let us try to deal with this term. So, instead of x 1 I am going to write it as x of t 1 here x 1 is nothing but x of t 1 right and then x not equals to i t 1 greater than or equals to u and then what I will now do is I know that at least my t 1 is going to be at least u that has been already told right. So, I am going to replace this t 1 here probability that x of u plus some y of u. Now, I have been also when I have been told that t 1 is going to be greater than or equals to u that means I have basically know my chain all the way up to u. So, this is correct. So, what I have used? I have been told that my t 1 is greater than or equals to some u. I know that my Markov chain sorry my CTMC is continue to stay in that state i at least till u and this t 1 I have split it into two parts i because t 1 I know is at least going to be greater than u yes that much of u and after that this is my residual time it is going to take at least larger than this before you are going to change your state. So, I can write my t 1 as these two component I can do that because t 1 is already been told me to be larger than this u okay fine. So, now what we will do is okay fine this has been given to me like this in this what has been observed. Now, I am going to so anyway that this part I have dealt with I have to deal with this probability here. This probability we will assume that by assuming the homogeneity property exploiting the homogeneity property that if I shift everything the whole process by u amount. So, u is a fixed quantity for me I am going to shift all this process by u amount the probability should not change. So, u to the power u and this one is like x of. So, this is I will set u to be 0 then this is like u of 0 taking value j and now this is like x of 0 is equals to u. What I have done is basically I have shifted my entire process to the origin that is why I am going to get my y of 0 that but I mean this is all just manipulation but now what you will see that once what is y of 0 condition that you already know that x of 0 equals to y what is how much time this is going to be it is going to be t1 right like if you are going to be how much more time you are going to need before you leave it minimum times. So, this is again x of t1 and this is j and this is x of 0 and according to our definition this is nothing but pij. So, what we have basically done here is to decouple these two process that was amount of time the probability that I am going to stay in this process at least for u amount and after that if I am going to look at probability of jumping to another state that is going to be still governed by my pij process. We can make some more observations here. So, now let us say that so, this is what we have so now let us see that what is that it is going to happen when AI is greater than 0. What is AI? AI is basically giving the rate at which I mean the amount of time that AI governs before you are going to leave state I right. Suppose let us say AI is going to be greater than 0 that means probability that you are going to stay at least for some amount in the state I is going to be positive right. If AI is going to be positive that like it is not like it is it is not at least instantaneous right instantaneous is the case when AI equals to is equals to infinity. Let us see that this is so AI greater than 0 allows me the possibility of taking AI to be infinity also right. So, whatever suppose AI equals to 0 what is this probability is going to be? Suppose let us say I started from state I and now I am looking at going to state J after the first jump. So, if my AI is going to be positive it must be the case that I would be jumping to some J other than I right like because if my J is by definition my x 1 is the state. So, here may be the importance of right and left continuity comes suppose if x 1 when time t 1 has already happened I am already assigned the state which is the new state that has been taken ok. So, I buy the time t 1 by definition I have moved to a next state. So, if this quantity is J 5 if my J is equal to i what is this probability is going to be? It is going to be 0 right because by t 1 by definition I am saying that I have left that state and gone to other state. So, only if J is not equal to i this is positive if again J equals to i like then this is a this is a 0 quantity. So, if for J equals to i let us say this guy is quantity is 0 and if AI is greater than 0 right at least what is this quantity is going to be some unless let us say this is also not equals to infinity. So, AI is some let us say finite quantity then this guy is not a 0 quantity then what is the only possibility it must be the case that PII is equals to 0 right. So, what is coming from the definition of Pij? Why is that? Oh right. So, what would we say t 1 is something it jump has happened right. So, if if I am looking at a some state which is other than i that is not going to happen right that is by definition. So, fine. So, we do not need to. So, I mean the same arguments we are applying here. So, we are going to say that this is going to 0 if J equals to i and this can be some non-zero quantity only if J is not equals to i ok. So, let us understand this suppose now. So, by this definition it looks like this should hold for all values of AI right whether the state i is absorbing or instantaneous. So, I really need to worry about whether this AI greater than or equals to 0. So, suppose my state is i is instantaneous. If my state is instantaneous what is t 1 going to be for that? t 1 is going to be 0 right like it is by definition of y t yeah it is going to be 0. So, in that case t 1 is going to be 0 here. So, I am just looking at why is that then x of 0 state i then it is going to be 0. I would ideally like that instantaneously like like suppose if my AI is equals to infinity that is my instantaneous case. So, in that case like this is like a probability of t 1 is like almost surely going to be 0 right in that case because t 1 in that case like i would be in this case and what this quantity I would like to be? I would like it to be 1 actually if J is equals to i is not it? So, we have started with instantaneously i oh no in that case it is going to be right 0 only because you are like leaving that state very very fast right like even t 1 is kind of 0 it is like instantaneous you are quickly leaving that. So, if J equals to i that is going to be 0 again so that is fine now let us consider a case where my state is absorbing when is my state is absorbing I said AI equals to 0 right. So, when my state is absorbing what is my t 1 is going to be my t n is going to be infinity right like. So, in that case what I will be looking at. So, I will be looking at basically equals to i and here what we are saying is is this still consistent here and i equals to J that is fine right like even when I am at very after large amount of time I am going to look for a different state but here that different is still happening only at infinity time so fine this is also fine. So, right we do not need to really worry about whether AI is is strictly positive or whatever. So, it appears like as long as any AI I am going to take this p ij happens to be p i 0 if i j equals to i ok. So, let us see that what the assumptions or whatever the arguments we have are going to be consistent here. Now, in this definition whatever I have here if I am going to just set u equals to 0 we already just saw that probability that my t n plus 1 minus t n greater than 0 then x 1 plus 1 is equals to 0 all the way up to x 0 x 1 to x n. What are these values? 0, v 1, t 1 all the way up to t n because u equals to 0 this is simply going to be now p ij right by our definition because e to the power a i u that has shrunk onto 1 and we are going to get this. And now suppose I am in the case of pure jump process right because of the pure jump process I am not living my state instantaneously. So, there should be gap between my nth and n plus 1 process jumps right because it is a pure jump process. So, I mean this is fine. So, this probability is nothing but simply then probability that x n plus 1 is equals to j that is not equals to i 0 all the way equals to i n t 1 equals to t. And this is in a way like same as what we have got here it is just like after shifting the t n process to the origin right. So, here I am just say ok x n plus 1th jump is going to take state i given that all the way up to this this is my p ij which is exactly nothing but this. So, now with this definition of p ij embedded process which we called as jump process with this let me call this as a metric transition probability matrix is it a DTMC. So, I have for my continuous time Markov chain I have derived an embedded chain which has this transition probability matrix p ij which I defined like this with this p ij's we are all in this setting let us assume time homogeneity and all.  So, you need to check this indeed it is true like you can show that like if I have an underlying if I focus on this underlying jump process and whatever the jump chains I have is going to be a Markov chain with respect to this transition probability matrix p. And henceforth we are going to simply recall going to call it as EMC that is embedded. So, we are looking even though looking at looked at a continuous process Markov chain, but what we actually did is we extracted a discrete version of this continuous time Markov chain which is called as embedded Markov chain. And what we are going to focus on here is kind of renewals here right. What are the renewals here? I am this particular stage I am going to take another stage before that I am going to spend some amount of time in this stage and after that I am again going to jump another state after spending certain amount of time. So, between these two jumps you can think that as a cycle and jumps you can think it as renewals right. So, basically what is this? This underlying embedded chain is a if you are going to look at this sequence these are what? These are the jump instances, but from this can derive your life cycles right like a lifetimes like the way we did earlier. Now, what are the distributions of this life cycles? Is there this life cycles have any distributions? So, what would we say? We have my ok let us take this I have already my CTMC my event happened at these points I looked at this time. So, this is some this defined my T1 this entire thing defined my T2 and all the way this defined up to my T3, but I could just focus on this U1 this interval U2 this interval and U3 this intervals and each one of them I could think of a cycle. Now, this interval what did govern it? What what did what govern the length of this interval? Suppose let us say at this point I am at state I ok. What did govern the length of this U3? That is U3, but what did govern it? Did it have any underlying distribution that governed what is the length of this U3 is? We just said it right already what did that govern it? So, what is this basically this is a sojourn time right the way we defined it U3 is the amount before you are going to make a change in your state. So, U3 is the sojourn time and we have just said that that has a exponential distribution, but with what parameter with the parameter ai which is state dependent that state I dependent. So, here what we have is we have basically renewals, but the length of that renewal cycle depends on from which state it started it right. So, when I defined the actual renewal process how did we define let us consider a sequence of UIs U1 all mutually independent and then we said U2 U3 are all also identically distributed, but here if you are going to look at U1 U2 U3 this sequence are they mutually independent they are right like once you know you are in this state Markov chain previous to that does not matter and I am going to state the next state I am going to focus on that that is independent. So, they are mutually independent are they identically distributed are they they are not right because every cycles the length of the distribution is going to depend on from which state they are going to start. So, I have a renewal process here like, but unlike in the our process where all my life cycles were have a identical distribution except maybe the possible first cycle subsequently everybody has same renewal it is not here it depends on which state you are going to start with ok. Now, let us focus on Poisson process. So, we know that Poisson process is a CTMC right we showed in the first class itself of this lecture about CTMC that if you are going to take a Poisson process it satisfies Markov property. Now, what is the state space of your Poisson process it is going to be natural numbers right you are just counting when the first one happened this is a counting process. So, it has to be all natural numbers. Now, if I say I have a Poisson process with parameter lambda whatever my life cycles distributions are exponential with what parameter lambda right. So, what is ai's in my Poisson process it is going to be lambda right and does it depend on which state you are in it is not like. So, you can just verify that if you have a Poisson process with rate lambda that means you have basically ai is equals to lambda for all life right. So, we have a Poisson process is a special CTMC in which all my ai's are that common parameter lambda, but if you have this different parameters ai then it is a more general CTMC. So, Poisson process is a special case of my CTMC in which all my ai's are the same value and depending on my sequence of ai's maybe I can get a different continuous time Markov chains. So, when the theory of this CTMC it is going to we are going to develop in a way very parallel to what we did for DTMC. So, now to understand all the properties of CTMC now we are going to only look at the properties of my DTMC because I know DTMC well we have already studied all its properties. So, now let us see whether there is a notion of transience recurrence in my CTMC also right and how to define them. So, is there a notion of communicating classes in my CTMC? So, do you think there should be a analogous version of communicating classes for the CTMC? So, let us see. So, what is this notion? i goes to j we will have the same interpretation as in DTMC i arrow j means i is reachable from j sorry j is reachable from i. So, we are going to say j is reachable from i if there exists some t positive such that pij of t is going to be positive and similarly we are going to show that we are going to say that i and j are reachable from each other if i is equals to and this is exactly what we had in our DTMC. But we are just now looking at earlier we wanted some positive n such that pij of n is positive, but now we want pij of t to be positive. So, like in DTMC we can also argue that this equivalence this relation is an equivalence class and it partitions all my states in my CTMC. Now, here is the theorem how to and we can define my communicating classes in terms of this equivalence classes set of all states which have satisfies this equivalence relation. Now, it so happens that the communicating class of my CTMC should be same as the communicating class in the underlying embedded Markov chain. So, a CTMC and its embedded Markov chain have so we know that both my CTMC and its underlying embedded Markov chains they have the same state space whatever the communicating class my embedded Markov chain has that is also going to be the communicating class for my CTMC. So, if I know my DTMC well the underlying embedded Markov chain I already know about my CTMC. So, I am not going to prove this it is just a brief proof in the book just look into that it is just like under the simple intuition that if in your DTMC if you have to reach from state i to j there should be some same finite amount of time in some finite amount of time you should be do with this some positive probability right. That means there is an that is like that many finite number of intervals should happen, but that finite number of intervals you can translate in a jump process to some finite time in your continuous CTMC. And you can come up with finite time under which you can go from state i to j ok. So, that is made bit more formal in the proof just look into that. So, now we know that my CTMC has an embedded Markov chains and it has an association transition probabilities Pijs which I can derive. Now, to define my CTMC what all the parameters I need. So, what are the properties what you feel so far are the characteristics of my CTMCs ok I have this P of t. So, my CTMC has this transition probability sorry my state space it has associated transition probability matrix for all P and let us also say I have my initial distribution. Now, this P of t from this I could derive my P which is my Pij. In addition to this was there any other characteristics of your CTMC that is associated with each of your states a i's right like there is an another parameters a i. So, depending on your a i's your CTMC could be different and it is not like this a i's are independent from this p t's they will be this p t's are going to influence how this a i's are going to look, but a i's are one of the important characteristics you just saw that for a Poisson process a i's simply lambda if a i's are different that is going to give a different CTMC. Now, in general and we also give a probability in which a i's and Pijs governed my transition from a given state to another state after spending certain amount of time in that state right. So, in a way Pijs and a i's kind of summarize the information I have in my p t and using this possibly I can describe my CTMC. So, now this is the question we want to make more precise. Given me CTMC P of t and my state space my initial distributions I have I can find out this ok. So, my CTMC defines these characteristics. Now, the other question is it possible that if you just give me this matrix P and this a i's can I have a CTMC that will define my CTMC. You understand the question? So, this is ok let us think of this these are two set of parameters. We initially said that ok let me for concateness also write all these distributions this is my initial distributions are known. From this we could derive these parameters. So, these parameters we said that this p t's and this x naught initial distribution they completely define my finite dimensional distributions. Once I have understanding of my finite dimensional distribution I know how my CTMC behave and these are like extracted features of this. Now, the question is this a complete characterization of my CTMC is it that if I just give you this parameter you can uniquely recover a CTMC with these parameters ok. In that case all I need to do is instead of giving this p t which is a which I have to specify for every t I will just specify this few parameters transition probability matrix and this a i parameters. Then is it sufficient to completely characterize my CTMC ok. I just want to say this in two minutes so that I finish what I planned today. I am just going to state it so that we can start with a fresh topic from next class. So, it so happens that suppose you have this quantity. So, what is this? This is the sum of your lifetime intervals right. So, this is like if you take n equals to 0 this will give the length of my first interval and then n equals to this will give me second interval. Let us say this is going to be psi. If somehow the expected value of this spans my entire line then from these parameters I could recover my CTMC complete characterization of. So, in a way like what are these? These are lifetimes right. These can be characterized in terms of my AIs and PIGs right because I do not know what state I am going to start with.  I could compute this Tn and Tn plus 1 right using these parameters. So, this is going to define these distributions and if it so happens that the expected value of this psi happens to be infinity then P that is my transition probability matrix A I am just going to call this as A enough to reconstruct. So, I will just leave it to read you it is a pretty straightforward why if this happens you can able to reconstruct your CTMC using these parameters otherwise why you cannot. If it so happens that if my epsilon psi is finite then you will not be able to reconstruct in a unique way your CTMC using these parameters alone. But if you so happens that this quantity happens to be infinity then these parameters are enough to reconstruct your CTMC in a unique fashion. But now we are going to say the pure jump process is called regular if psi equals to infinity with probability 1. Now, suppose psi is not equals to infinity here is not finite here that means psi is extends entire real line right. Then that means this difference the lifetimes they have span the entire real line. So, then looking at this process I could define a process of every possible t right if it has expand the entire real line had it been finite I could know the process only for finite t but not entire thing. But if it happens to be infinity with probability 1 I could with probability 1 I could define it for all the point x t. So, that is what this condition is requiring it should be the case that if this psi equals to infinity with probability 1 then we are going to call it as a regular 1 and we will be just focusing on that. So, let us take an example. So, if I have a Poisson process is it a regular process? Let us say Poisson with rate lambda Poisson with rate lambda what? So, just take the expectation of that this is expectation of this difference let us say I could interchange this infinite summation and expectation after some argument. Then expected difference of this is nothing but expected value of an exponential random variable with rate lambda right. So, you are just adding lambda infinitely many times that means this quantity is already in. So, if I have a Poisson process with lambda strictly positive that is already a regular process. Now, what else could be a regular process? It so happens that any CTMC which takes values in a finite state space is going to be a pure jump process which is going to take value in a finite state space is always going to be a regular process. Why is that? So, now, so I am going to just write it before I say that. So, this is a statement for a pure jump there exists some new positive such that this quantity is ai this is going to be new for all i then just border on this like we are just saying that if all the ai's. So, remember this quantity is ai's which governed your Sojourn times they can be any quantities between 0 to infinity based on that we have said they are either absorbing stable or instantaneous right. But suppose if this ai quantities happens to be uniformly upper bounded then it must be the case that your process is going to be always regular process this holds true. I mean this needs a couple of line of proof, but let us skip this. So, let us understand that as long as my ai's are all bounded it is going to be a regular process. For example, in the Poisson trace you are going to say Poisson process with rate lambda you know that ai's equals to what? For the Poisson process for the Poisson process ai equals to lambda for all i right. So, lambda is an uniform upper bound in that case for your Poisson process. So, this condition already holds and it is we already I will do that Poisson process is a regular process. Now, as a corollary to this. So, like most of the things I am going to now discuss in the CTMC we are just going to state the results and with respect to Poisson process we will understand the result. But even though they hold in a more not necessarily just for Poisson process like more general continuous time approaches. So, as a corollary to this if CTMC I am going to say always we are assuming that pure jump CTMC with finite is regular is this obvious this corollary now. So, I am saying that my CTMC takes only finite number of states and it is a pure jump CTMC. So, ai is not allowed to take infinity right it can be either 0 or some positive, but bounded value. So, then in that case I can always come up with a uniform bound on finitely many ai's right. And in that case I will have always such a nu I will find it and that is why I can appeal to this theorem and I can claim that my CTMC is regular. Okay, another result is so you need to like the go through quickly the proofs of this given the book like we are not lengthy they are just like couple of lines. But the point is you need to know these properties. So, that you can you are free to use these properties wherever in whichever problem you like. But you need to tell clearly before you applying this results you need to make sure that all the hypothesis are satisfied then you can appeal to that. For example, if you want to apply this theorem, you need to first tell me what is that nu uniform bound on all this then you can say fine I am going to then I am going to clear it is a regular. But before that you need to give me the value of nu it just saying there exists right. But if you are going to use this value you need to demonstrate existence of such a nu value. Okay, another thing is pure jump embedded marker chain is recurrent. Does this theorem make sense intuitively at least what we are saying? Okay, take your CTMC look at its embedded marker chain and if that embedded marker chain has happens to be recurrent then your CTMC is also regular. Does that make sense? So, like now let us say once I said my embedded marker chain is recurrent right that means I am going to revisit my state infinitely often times right. So, that is the definition of my recurrence. I am going to keep revisiting my states in my embedded marker chain that state again and again. If I am going to coming back to that state again and again that means you are going to first leave it in your continuous marker chain and then coming back to that state. And this is happening repeatedly that means in some way it must be the case that this process is like a spanning spanning the entire real life.  So, this is happening and because of that the lifetimes in that states they are going to add so many times to this and it is like a pure gem process. So, you are going to see that that expected value of y is going to be finite. This is just like broad level idea and that you can make this bit more formal. So, in either of this case either you can show that there is a uniform bound on AS or your state space is finite or you can show that my embedded marker chain is a recurrent then it is automatic that your process is going to be regular. In that case all you need to focus on is all you need is this information about all to generate your process x t which is uniquely represents the process with the underlying parameters.