A critical branching process with immigration in random environment

2020/03/14 by Valeriy Ivanovich Afanasyev, Afanasyev, V. I.
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60J80 #60K37 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2003.06590

openalex publication_date 2020/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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