Affiliation:
1. Steklov Mathematical Institute of Russian Academy of Sciences , Moscow , Russia
Abstract
Abstract
A multi-type branching process evolving in a random environment generated by a sequence of independent identically distributed random variables is considered. The asymptotics of the survival probability of the process for a long time is found under the assumption that the matrices of the mean values of direct descendants have a common left eigenvector and the increment X of the associated random walk generated by the logarithms of the Perron roots of these matrices satisfies conditions E
X < 0 and E
XeX
> 0.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
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