Poisson process approximation: From Palm theory to Stein’s method

Abstract

This exposition explains the basic ideas of Stein's method for Pois- son random variable approximation and Poisson process approximation from the point of view of the immigration-death process and Palm theory. The latter approach also enables us to define local dependence of point processes (Chen & Xia (2004)) and use it to study Poisson process approximation for locally dependent point processes and for dependent superposition of point processes. 1. Poisson approximation Stein's method for Poisson approximation was developed by Chen (1975) which is based on the following observation: a nonnegative integer valued random variable W follows Poisson distribution with mean , denoted as Po( ), if and only if