Moments and large deviations for supercritical branching processes with immigration in random environments

被引：0
作者：
Chunmao Huang
Chen Wang
Xiaoqiang Wang
机构：
[1] Harbin Institute of Technology (Weihai),Department of Mathematics
[2] Sun Yat-sen University,School of Data and Computer Science
[3] Shandong University,School of Mathematics and Statistics
来源：
Acta Mathematica Scientia | 2022年 / 42卷
关键词：
branching process with immigration; random environment; moments; harmonic moments; large deviations; 60J80; 60K37; 60F10;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：49 / 72
页数：23
相关论文
共 70 条
[1]  
Athreya K B(1994)Large deviation rates for branching processes I: Single type case Annals of Applied Probability 4 779-790
[2]  
Athreya K B(1971)On branching processes with random environments I: Extinction probabilities The Annals of Mathematical Statistics 42 1499-1520
[3]  
Karlin S(1971)Branching processes with random environments II: Limit theorems The Annals of Mathematical Statistics 42 145-152
[4]  
Athreya K B(2009)Cell contamination and branching processes in a random environment with immigration Advances in Applied Probability 41 1059-1081
[5]  
Karlin S(2009)Large deviations for branching processes in random environment Markov Processes and Related Fields 15 493-524
[6]  
Bansaye V(2011)Upper large deviations for branching processes in random environment with heavy tails Electronic Journal of Probability 16 1900-1933
[7]  
Bansaye V(2013)Lower large deviations for supercritical branching processes in random environment Proc Steklov Inst Math 282 15-34
[8]  
Berestycki J(2014)Small positive values for supercritical branching processes in random environment Ann Inst H Poincaré Probab Statist 50 770-805
[9]  
Bansaye V(2017)On the survival probability for a class of subcritical branching processes in random environment Bernoulli 23 58-88
[10]  
Böinghoff C(2015)On large deviations of a branching process in random environments with immigration at moments of extinction Discrete Math Appl 25 339-343
1234567