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Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero

Author

Listed:
  • Doudou Li

    (Beijing Normal University)

  • Vladimir Vatutin

    (Steklov Mathematical Institute)

  • Mei Zhang

    (Beijing Normal University)

Abstract

We consider the subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the moment when first invader (or invaders) came to an empty site until the moment when the site becomes empty again. We prove that the tail distribution decays with exponential rate. The main tools are change of measure and some conditional limit theorems for random walks.

Suggested Citation

  • Doudou Li & Vladimir Vatutin & Mei Zhang, 2021. "Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero," Journal of Theoretical Probability, Springer, vol. 34(2), pages 874-896, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00991-5
    DOI: 10.1007/s10959-020-00991-5
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    References listed on IDEAS

    as
    1. Vatutin, Vladimir & Zheng, Xinghua, 2012. "Subcritical branching processes in a random environment without the Cramer condition," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2594-2609.
    2. V. I. Afanasyev & C. Böinghoff & G. Kersting & V. A. Vatutin, 2012. "Limit Theorems for Weakly Subcritical Branching Processes in Random Environment," Journal of Theoretical Probability, Springer, vol. 25(3), pages 703-732, September.
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