Exact convergence rate in the central limit theorem for a branching process in a random environment

Zhi-Qiang Gao

Statistics & Probability Letters, 2021, vol. 178, issue C

Abstract: Let {Zn} be a supercritical branching process in an independent and identically distributed random environment. As is well known, the behavior of Zn depends primarily on that of the associated random walk Sn constructed by the logarithms of the quenched expectation of population sizes. By this observation, the Berry–Esséen bound for logZn has been established by Grama et al. (2017). To refine that, we figure out the exact convergence rate in the central limit theorem for logZn under the annealed law, with less restrictive moment conditions. In particular, there is one factor in the rate function concerning on logZn that does not appear in that for Sn. Hence the result indicates the essential difference between logZn and Sn.

Keywords: Branching processes in random environments; Central limit theorem; Berry–Esseen bound; Exact convergence rate (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109194

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