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On the maximum of a subcritical branching process in a random environment

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  • Afanasyev, V. I.

Abstract

Let {[xi]n} be a subcritical branching process in random environment with independent identically distributed generating functions fn(s). It is shown that if there exists a positive number æ such that E(f0'(1))æ=1 then, for x-->+[infinity],where K is a positive constant.

Suggested Citation

  • Afanasyev, V. I., 2001. "On the maximum of a subcritical branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 87-107, May.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:87-107
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    References listed on IDEAS

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    1. Tanny, David, 1988. "A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 123-139, April.
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    Cited by:

    1. Chen, Dayue & de Raphélis, Loïc & Hu, Yueyun, 2018. "Favorite sites of randomly biased walks on a supercritical Galton–Watson tree," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1525-1557.
    2. Gantert, Nina & Shi, Zhan, 2002. "Many visits to a single site by a transient random walk in random environment," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 159-176, June.

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