Berry-Esseen’s bound for a superadditive bisexual branching process in a random environment

Sheng Xiao and Xiangdong Liu

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 1, 98-114

Abstract: Let (Zn) be a superadditive bisexual branching process in an independent and identically distributed (i.i.d.) random environment. We give the estimators for the mean of the conditional mean growth rate and the mean of the logarithm of the conditional mean growth rate. We establish the central limit theorems and Berry-Esseen bounds for ∑k=0n−1(Zk+1/Zk) and log⁡Zn under the annealed law ℙ. To this end, we present a martingale and investigate its limiting properties; we show the non degeneration of the limit variable of normalized population size.

Date: 2025
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DOI: 10.1080/03610926.2024.2301991

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