Stationarity
A point process is said to be stationary if has the same distribution as for all For a stationary point process, the mean measure for some constant and where stands for the Lebesgue measure. This is called the intensity of the point process. A stationary point process on has almost surely either 0 or an infinite number of points in total. For more on stationary point processes and random measure, refer to Chapter 12 of Daley & Vere-Jones. It is to be noted that stationarity has been defined and studied for point processes in more general spaces than .
Read more about this topic: Point Process, General Point Process Theory