NON-UNIFORM BERRY-ESSEEN-TYPE INEQUALITIES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT

被引：0

作者：

Wang, X. I. A. O. Q. I. A. N. G. ^{[1
]}

Wu, J. I. U. J. I. A. N. G. ^{[2
]}

Huang, C. H. U. N. M. A. O. ^{[2
]}

机构：

[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Peoples R China

[2] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2023年 / 17卷 / 01期

关键词：

Branching process with immigration; random environment; central limit theo-rem; Berry-Esseen inequality; LARGE DEVIATION RATES; GALTON-WATSON PROCESS; LIMIT-THEOREMS; MOMENTS;

D O I：

10.7153/jmi-2023-17-22

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Wn be the fundamental submartingale of a supercritical branching process with immigration in a random environment. In order to characterize the convergence rates of Wn , the quenched and annealed non-uniform Berry-Esseen-type inequalities are established for Wn+k - Wn for each fxed k is an element of {1,2, center dot center dot center dot , infinity}, which reveal the convergence rates of the corresponding central limit theorems.

引用

页码：325 / 339

页数：15