Getting minimum value at a given time in SQL
<p>I have the following SQL table:</p>

<pre><code>start_time          end_time            value
2016-01-01 00:00:00 2016-01-01 08:59:59 1
2016-01-01 06:00:00 2016-01-01 14:59:59 2
2016-01-01 12:00:00 2016-01-01 17:59:59 1.5
2016-01-01 03:00:00 2016-01-01 17:59:59 3
</code></pre>

<p>I want to convert it into:</p>

<pre><code>start_time          end_time            min_value
2016-01-01 00:00:00 2016-01-01 08:59:59 1
2016-01-01 09:00:00 2016-01-01 11:59:59 2
2016-01-01 12:00:00 2016-01-01 17:59:59 1.5
</code></pre>

<p>where <code>min_value</code> is the minimum <code>value</code> at a given point in time. Is it possible to do this in SQL?</p>