Moments and Large Deviations for Supercritical Branching Processes with Immigration in Random Environments

被引：8

作者：

Huang, Chunmao ^{[1
]}

Wang, Chen ^{[2
]}

Wang, Xiaoqiang ^{[3
]}

机构：

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

[2] Sun Yat Sen Univ, Sch Data & Comp Sci, Guangzhou 510006, Peoples R China

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

来源：

ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 01期

关键词：

branching process with immigration; random environment; moments; harmonic moments; large deviations; LIMIT-THEOREMS; HARMONIC MOMENTS; RATES;

D O I：

10.1007/s10473-022-0102-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (Z(n)) be a branching process with immigration in a random environment xi, where xi is an independent and identically distributed sequence of random variables. We show asymptotic properties for all the moments of Z(n) and describe the decay rates of the n-step transition probabilities. As applications, a large deviation principle for the sequence log Z(n) is established, and related large deviations are also studied.

引用

页码：49 / 72

页数：24

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