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

• 作者: Chunmao HUANG Chen WANG Xiaoqiang WANG
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 49-72
• 页数: 24页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2022.01.002

摘要

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.