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

Xulan Huang, Yingqiu Li and Kainan Xiang

Statistics & Probability Letters, 2022, vol. 190, issue C

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.

Keywords: Branching processes with immigration; Random environment; Submartingale; Rate of convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109619

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