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<p>We consider the Galton–Watson branching processes with immigration, in which the mathematical expectation A of the number of offspring of a single individual tends to unity. For the process denoting the number of individuals that existed before the generation n (total progeny) normalized by mathematical expectation, we find an asymptotic distribution that depends on the rate at which A tends to unity.</p>

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Transient Phenomena for Total Progeny in Galton–Watson Branching Processes with Immigration

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • T. B. Lysetskyi,
  • Ya. I. Yeleiko

摘要

We consider the Galton–Watson branching processes with immigration, in which the mathematical expectation A of the number of offspring of a single individual tends to unity. For the process denoting the number of individuals that existed before the generation n (total progeny) normalized by mathematical expectation, we find an asymptotic distribution that depends on the rate at which A tends to unity.