A critical branching process with immigration in random environment

V.I. Afanasyev

Stochastic Processes and their Applications, 2021, vol. 139, issue C, 110-138

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.

Keywords: Branching process in random environment; Branching process with immigration; Functional limit theorem (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.05.001

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