These processes are used to describe the arrival of customers to a store or a queue.
This type of model can be generalized through Cinlar's inversion method or by thinning. It's not Brownian motion, but these systems have the predictable representation property. The probability of finding two events separated by a given time in these systems is exponentially distributed and like other systems in its class it posses independent increments. This is a simple example of a Levy process where each jump increments the count by one. This memoryless counting process starts at zero and the number of events n in any length of time t is equal to e to the negative lambda t times lambda t raised to the n over n factorial. These processes are used to describe the arrival of customers to a store or a queue. For 10 points, name these processes that are governed a distribution of the same name where events are independent but happen at an average rate lambda.
This type of model can be generalized through Cinlar's inversion method or by thinning.
Poisson process [prompt on Levy process; prompt on exponential process]