Multi-type subcritical branching processes in a random environment

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 distribut...

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Published in:Advances in applied probability 2018-12, Vol.50 (A), p.281-289
Main Authors: Vatutin, Vladimir, Wachtel, Vitali
Format: Article
Language:English
Subjects:
Asymptotic properties
Branching (mathematics)
Markov processes
Original Article
Probability
Random walk theory
Survival
Theorems
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description 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.
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subjects Asymptotic properties
Branching (mathematics)
Markov processes
Original Article
Probability
Random walk theory
Survival
Theorems
title Multi-type subcritical branching processes in a random environment
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