On the structure of regular infinitely divisible point processes

Abstract

A representation for the probability generating functional (p.g.fl.) of a regular infinitely divisible (i.d.) stochastic point process, motivated as a generalization of the Gauss-Poisson process, is presented. The functional is characterized by a sequence of Borel product measures. Necessary and sufficient conditions, in terms of these Borel measures, are given for this representation to be a p.g.fl., thus characterizing all regular i.d. point processes.