MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

doi:10.1007/s10473-022-0102-3

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 49-72.doi: 10.1007/s10473-022-0102-3

MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

黄春茂¹, 王晨², 王效强³

1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China;
2. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China;
3. School of Mathematics and Statistics, Shandong University, Weihai, 264209, China

收稿日期:2020-08-20 修回日期:2021-05-21 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Xiaoqiang WANG,E-mail:xiaoqiang.wang@sdu.edu.cn E-mail:xiaoqiang.wang@sdu.edu.cn
作者简介:Chunmao HUANG,E-mail:cmhuang@hitwh.edu.cn;Chen WANG,E-mail:wangch329@mail2.sysu.edu.cn
基金资助:
This work was partially supported by the National Nature Science Foundation of China (11601286, 11501146).

MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

Chunmao HUANG¹, Chen WANG², Xiaoqiang WANG³

1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China;
2. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China;
3. School of Mathematics and Statistics, Shandong University, Weihai, 264209, China

Received:2020-08-20 Revised:2021-05-21 Online:2022-02-25 Published:2022-02-24
Contact: Xiaoqiang WANG,E-mail:xiaoqiang.wang@sdu.edu.cn E-mail:xiaoqiang.wang@sdu.edu.cn
Supported by:
This work was partially supported by the National Nature Science Foundation of China (11601286, 11501146).

摘要/Abstract

摘要： Let (Z_n) be a branching process with immigration in a random environment ξ, where ξ 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.

关键词: branching process with immigration, random environment, moments, harmonic moments, large deviations

Abstract: Let (Z_n) be a branching process with immigration in a random environment ξ, where ξ 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.

Key words: branching process with immigration, random environment, moments, harmonic moments, large deviations

中图分类号:

60J80

黄春茂, 王晨, 王效强. MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS[J]. 数学物理学报(英文版), 2022, 42(1): 49-72.

Chunmao HUANG, Chen WANG, Xiaoqiang WANG. MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS[J]. Acta mathematica scientia,Series B, 2022, 42(1): 49-72.

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MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

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