Random Space Change for Multiparameter Point Processes

Abstract

A way of transforming a multiparameter point process into a Poisson process is given. As in the one-parameter case, the compensator characterization of the Poisson process plays an important role in random space change for the multiparameter point process. We use the characterization of planar Poisson processes in terms of the 1-compensator by Brown to derive random space-change theorems. The results obtained hold under weaker conditions than those in Merzbach and Nualart.