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Evolution of branching processes in a random environment

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Abstract

This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in independent and identically distributed random environments. This is a natural generalization of the time-inhomogeneous branching processes. The key assumptions of the family of population models in question are nonoverlapping generations and discrete time. The reader should be aware of the fact that there are many very interesting papers covering other issues in the theory of branching processes in random environments which are not mentioned here.

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Authors and Affiliations

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

    V. A. Vatutin & E. E. Dyakonova

  2. Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96, Gothenburg, Sweden

    S. Sagitov

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  1. V. A. Vatutin
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  2. E. E. Dyakonova
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  3. S. Sagitov
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Correspondence to V. A. Vatutin.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 282, pp. 231–256.

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Vatutin, V.A., Dyakonova, E.E. & Sagitov, S. Evolution of branching processes in a random environment. Proc. Steklov Inst. Math. 282, 220–242 (2013). https://doi.org/10.1134/S0081543813060187

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