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On asymptotic behavior of time of extinction of critical bisexual branching process in random environment

Anton Zhiyanov & Alexander Viktorovich Shklyaev

Journal of Applied Probability2026https://doi.org/10.1017/jpr.2025.10072article
AJG 2ABDC A
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0.50

Abstract

We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs N , we prove that its extinction time is of order $\ln^2 N$ . Interestingly, this result is valid for a general class of mating functions. Among these are the functions describing the monogamous and polygamous behavior of couples, as well as the function reducing the bisexual branching process to the simple one.

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https://doi.org/https://doi.org/10.1017/jpr.2025.10072

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@article{anton2026,
  title        = {{On asymptotic behavior of time of extinction of critical bisexual branching process in random environment}},
  author       = {Anton Zhiyanov & Alexander Viktorovich Shklyaev},
  journal      = {Journal of Applied Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1017/jpr.2025.10072},
}

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On asymptotic behavior of time of extinction of critical bisexual branching process in random environment

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0.50

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
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