A characterization of non-homogeneous poisson processes

Abstract

The arrival times for a large number q of independent replications of a simple point processes on [0,1] are ranked. Let {ni;i=l,...,^f} be the number of arrivals for each replication. The ranks are randomly distributed if their distribution among the replications is the same as that obtained by drawing groups of {nj?=1 balls randomly and without replacement from an urn containing n = Yj = \n{ balls marked with ranks {1,2, ...,n}. It is shown that randomly distributed ranks characterizes the class of non-homogeneous Poisson processes.

Keywords:

• Non-homogeneous Poisson process
• randomness
• ranks

^†Research supported in part by NSERC Grant A4551.

^†Research supported in part by NSERC Grant A4551.

Notes

^†Research supported in part by NSERC Grant A4551.