A.s. convergence rate for a supercritical branching processes with immigration in a random environment

被引：6

作者：

Li, Yingqiu ^{[1
]}

Huang, Xulan ^{[1
]}

机构：

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

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2022年 / 51卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Branching process; immigration; varying environment; random environment; submartingale; convergence rate;

D O I：

10.1080/03610926.2020.1756330

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 be a supercritical branching process with immigration in a random environment xi. We are interested in the almost sure (a.s.) convergence rate of the submartingale to its limit where is an usually used norming sequence. The result about convergence a.s. are as following. Under a moment condition of order and where, a.s. for some a > 0 that we find explicity; then assuming for some we have a.s.; similar conclusions hold in a varying environment, but the condition will be replaced by where is a positive sequence of real numbers.

引用

页码：826 / 839

页数：14

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