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A critical branching process with immigration in random environment

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  • Afanasyev, V.I.

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.

Suggested Citation

  • Afanasyev, V.I., 2021. "A critical branching process with immigration in random environment," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 110-138.
    • Handle: RePEc:eee:spapps:v:139:y:2021:i:c:p:110-138
    DOI: 10.1016/j.spa.2021.05.001
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