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Mat. Zametki, 2020, Volume 107, Issue 2, Pages 163–177 (Mi mz12395)  

The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment

V. A. Vatutin, E. E. D'yakonova

Novosibirsk State University

Abstract: The asymptotic behavior of the survival probability for multi-type branching processes in a random environment is studied. In the case where all particles are of one type, the class of processes under consideration corresponds to intermediately subcritical processes. Under fairly general assumptions on the form of the generating functions of the laws of reproduction of particles, it is proved that the survival probability at a remote instant $n$ of time for a process that started at the zero instant of time from one particle of any type is of the order of $\lambda^{n}n^{-1/2}$, where $\lambda \in (0,1)$ is a constant defined in terms of the Lyapunov exponent for products of the mean-value matrices of the laws of reproduction of particles.

Keywords: branching process, random environment, survival probability, intermediately subcritical process, change of measures.

Funding Agency Grant Number
Russian Science Foundation 17-11-01173
This work was supported by the Russian Science Foundation under grant 17-11-01173.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12395

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English version:
Mathematical Notes, 2020, 107:2, 189–200

Bibliographic databases:

UDC: 519.21
Received: 29.03.2019
Revised: 12.07.2019

Citation: V. A. Vatutin, E. E. D'yakonova, “The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment”, Mat. Zametki, 107:2 (2020), 163–177; Math. Notes, 107:2 (2020), 189–200

Citation in format AMSBIB
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\paper The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment
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\vol 107
\issue 2
\pages 163--177
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\jour Math. Notes
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\vol 107
\issue 2
\pages 189--200
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