Berry–Esseen bound for a supercritical branching processes with immigration in a random environment

Abstract

Let (Zn) be a supercritical branching process with immigration (Yn) in an independent and identically distributed environment ξ. We consider the rate of convergence of the normalized population Wn=Zn/Πn to its limit W, where (Πn) is the usually used norming sequence, and establish a Berry–Esseen bound. Similar results are also obtained for Wn+k−Wn for each fixed positive integer k.