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

被引：0

作者：

Li, Yingqiu ^{[1
,3
]}

Zhang, Xin ^{[1
]}

Lu, Zhan ^{[1
]}

Xiao, Sheng ^{[2
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China

[2] Hunan First Normal Univ, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China

[3] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2025年 / 216卷

基金：

中国国家自然科学基金;

关键词：

Branching processes; Random environment; Martingale; Polynomial convergence rate; Exact convergence rate; LARGE DEVIATIONS; MOMENTS;

D O I：

10.1016/j.spl.2024.110268

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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

引用

页数：9

共 18 条

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