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Subcritical branching processes in a random environment without the Cramer condition

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  • Vatutin, Vladimir
  • Zheng, Xinghua
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    Abstract

    A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of particles up to moment n given survival to this moment. Contrary to other types of subcritical BPRE, the limiting distribution is not discrete. We also show that the process survives for a long time owing to a single big jump of the associate random walk accompanied by a population explosion at the beginning of the process.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912000695
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 7 ()
    Pages: 2594-2609

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2594-2609

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    Related research

    Keywords: Branching process; Random environment; Random walk; Survival probability; Functional limit theorem;

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    1. Bansaye, Vincent, 2009. "Surviving particles for subcritical branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2436-2464, August.
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