Chapter 7 Point Process Analysis

A point process is a stochastic process that one can think of as “dropping down points” in a domain. For now, we will think of the domain as the real line which will represent time. Therefore, a point process is a stochastic process that drops “events” randomly down on to a time line. The key here is that the time at which events occur is random.

A point process can be thought of as a measure $N$ such that $N(A)$ is the number of points of the process that lie in the set $A$. On the real line, we can say that $N(a,b]$ is the number of points of the process that lie between $a$ and $b$.