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

Let (Zn) be a branching process with immigration in a random environment ζ,where ζ 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...

Full description

Saved in:
Bibliographic Details
Published in数学物理学报（英文版） Vol. 42; no. 1; pp. 49 - 72
Main Authors Chunmao HUANG, Chen WANG, Xiaoqiang WANG
Format Journal Article
LanguageEnglish
Published Department of Mathematics,Harbin Institute of Technology (Weihai),Weihai 264209,China%School of Data and Computer Science,Sun Yat-sen University,Guangzhou 510006,China%School of Mathematics and Statistics,Shandong University,Weihai 264209,China 2022
Subjects
large deviations
branching process with immigration
moments
random environment
harmonic moments
Online AccessGet full text

Cover

More Information
Summary:Let (Zn) be a branching process with immigration in a random environment ζ,where ζ 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.
ISSN:0252-9602
DOI:10.3969/j.issn.0252-9602.2022.01.002