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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Bibliographic Details
Published inAdvances in applied probability Vol. 50; no. A; pp. 281 - 289
Main Authors Vatutin, Vladimir, Wachtel, Vitali
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2018
Subjects
Asymptotic properties
Branching (mathematics)
Markov processes
Original Article
Probability
Random walk theory
Survival
Theorems
Branching process
Primary 60J80
Secondary 60F99
random environment
survival probability
conditional limit theorem
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2018.86