2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124745This exposition explains the basic ideas of Stein's method for Poisson 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 and Xia (2004)] and use it to study Poisson process approximation for locally dependent point processes and for dependent superposition of point processes.Published at http://dx.doi.org/10.1214/074921706000001076 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60--02 (Primary) 60F05, 60G55 (Secondary)text