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Limit theorems for decomposable branching processes in a random environment

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  30 March 2016

Vladimir Vatutin  and
Quansheng Liu
Vladimir Vatutin*
Affiliation:
Steklov Mathematical Institute
Quansheng Liu*
Affiliation:
Université de Bretagne-Sud
*
∗ Postal address: Steklov Mathematical Institute, Gubkin str. 8, 119991, Moscow, Russia. Email address: vatutin@mi.ras.ru
∗∗ Postal address: Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France.
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Abstract

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We study the asymptotics of the survival probability for the critical and decomposable branching processes in a random environment and prove Yaglom-type limit theorems for these processes. It is shown that such processes possess some properties having no analogues for the decomposable branching processes in a constant environment.

Keywords

Decomposable branching processessurvival probabilityrandom environment

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F17: Functional limit theorems; invariance principles 60J85: Applications of branching processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 877 - 893
Copyright
Copyright © 2015 by the Applied Probability Trust 

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