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 Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 4, Pages 634–653 (Mi tvp5146)

Multitype branching processes in random environment: survival probability for the critical case

V. A. Vatutin, E. E. D'yakonova

Novosibirsk State University

Abstract: We investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in an environment generated by a sequence of independent identically distributed random variables. Under fairly general assumptions on the form of the offspring generating functions of particles, we show that the probability of survival up to generation $n$ of the process initiated at moment zero by a single particle of type $i$ is equivalent to $\beta_in^{-1/2}$, where $\beta_i$ is a positive constant. This assertion essentially generalizes a number of previously known results.

Keywords: branching processes, random environment, survival probability, change of measure.

 Funding Agency Grant Number Russian Science Foundation 17-11-01173 This research was supported by the Russian Science Foundation (project no.~17-11-01173).

DOI: https://doi.org/10.4213/tvp5146

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English version:
Theory of Probability and its Applications, 2018, 62:4, 506–521

Bibliographic databases:

Citation: V. A. Vatutin, E. E. D'yakonova, “Multitype branching processes in random environment: survival probability for the critical case”, Teor. Veroyatnost. i Primenen., 62:4 (2017), 634–653; Theory Probab. Appl., 62:4 (2018), 506–521

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tvp5146
• https://doi.org/10.4213/tvp5146
• http://mi.mathnet.ru/eng/tvp/v62/i4/p634

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This publication is cited in the following articles:
1. E. Le Page, M. Peigné, C. Pham, “The survival probability of a critical multi-type branching process in i.i.d. random environment”, Ann. Probab., 46:5 (2018), 2946–2972
2. V. Vatutin, V. Wachtel, “Multi-type subcritical branching processes in a random environment”, Adv. Appl. Probab., 50:A (2018), 281–289
3. V. A. Vatutin, E. E. D'yakonova, “The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment”, Math. Notes, 107:2 (2020), 189–200
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