Central Limit Theorems for Cluster Point Processes

Abstract

An interesting class of stationary point processes on R d is the class of Poisson cluster processes. Consider a parent process N and a countable sequence of independent and identically distributed (i.i.d.) point processes Y i on R d . Each point mass x in N is replaced by an independent copy of Y centered at x. If N is a Poisson process, the resulting point process X is said to be a Poisson cluster point process (Poisson C.P.P.).