A critical branching process with immigration in random environment

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:139

Article

Afanasyev, V., I¹ 

[1] Russian Acad Sci, Steklov Math Inst, 8 Gubkin St, Moscow 119991, Russia

关键词: Branching process in random environment;    Branching process with immigration;    Functional limit theorem;   

DOI  :  10.1016/j.spa.2021.05.001

来源: Elsevier

【 摘 要 】

A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is normalized by a random coefficient depending on the random environment only. The distribution of the limiting process is described in terms of a strictly stable Levy process and a sequence of independent and identically distributed random variables which is independent of this process. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free