Exact convergence rate of the central limit theorem and polynomial convergence rate for branching processes in a random environment

Yingqiu Li, Xin Zhang, Zhan Lu and Sheng Xiao

Statistics & Probability Letters, 2025, vol. 216, issue C

Abstract: Let (Zn) be a supercritical branching process in an independent and identically distributed (i.i.d.) random environment. The paper studies the properties of the estimator Mn=n−1∑k=0n−1(Zk+1/Zk) introduced by Dion and Esty in 1979. We introduce a related martingale and discuss its convergence and exponential convergence rate. On this basis the exact convergence rate of the central limit theorem for normalized Mn is given.

Keywords: Branching processes; Random environment; Martingale; Polynomial convergence rate; Exact convergence rate (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110268

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