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

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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. 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. 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: Let (Zn) 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 Zn and describe the decay rates of the n-step transition probabilities. As applications, a large deviation principle for the sequence log Zn 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 (Zn) 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 Zn and describe the decay rates of the n-step transition probabilities. As applications, a large deviation principle for the sequence log Zn 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