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Multitype subcritical branching processes in a random environment

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Abstract

We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable Xe X has zero mean, we find the asymptotics of the survival probability at time n as n → ∞.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    E. E. Dyakonova

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  1. E. E. Dyakonova
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Correspondence to E. E. Dyakonova.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 282, pp. 87–97.

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Dyakonova, E.E. Multitype subcritical branching processes in a random environment. Proc. Steklov Inst. Math. 282, 80–89 (2013). https://doi.org/10.1134/S0081543813060084

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  • DOI: https://doi.org/10.1134/S0081543813060084

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