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Multi-type subcritical branching processes in a random environment

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  01 February 2019

Vladimir Vatutin  and
Vitali Wachtel
Vladimir Vatutin*
Affiliation:
Novosibirsk State University and Steklov Mathematical Institute
Vitali Wachtel*
Affiliation:
Universität Augsburg
*
Steklov Mathematical Institute, Gubkin Street 8, 119991 Moscow, Russia. Email address: vatutin@mi.ras.ru
Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany. Email address: vitali.wachtel@mathematik.uni-augsburg.de
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Abstract

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We study the asymptotic behavior of the survival probability of a multi-type branching process in a random environment. In the one-dimensional situation, the class of processes considered corresponds to the strongly subcritical case. We also prove a conditional limit theorem describing the distribution of the number of particles in the process given its survival for a long time.

Keywords

Branching processrandom environmentsurvival probabilityconditional limit theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F99: None of the above, but in this section
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 281 - 289
Copyright
Copyright © Applied Probability Trust 2018 

References

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