An invariance property of Poisson processes

Abstract

In this paper we shall investigate point processes generated by random variables of the form 〈g_i(T_i]), i=± 1, ± 2, … 〉, where 〈T_i, i= ± 1, … 〉 is the set of arrival times from a (not necessarily homogeneous) Poisson process or mixture of Poisson processes, and 〈g_i, i = ± 1, … 〉 is an independently and identically distributed (i.i.d.) or interchangeable sequence of random functions, independent of 〈T_i〉.