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 Diskr. Mat.: Year: Volume: Issue: Page: Find

 Diskr. Mat., 2019, Volume 31, Issue 3, Pages 26–46 (Mi dm1581)

Multitype weakly subcritical branching processes in random environment

V. A. Vatutin, E. E. D'yakonova

Novosibirsk State University

Abstract: A multi-type branching process evolving in a random environment generated by a sequence of independent equally distributed random variables is considered. The asymptotic of the survival probability of the process at a distant moment is found under the assumption that the mean matrices of the process have a common left eigenvector and the increment $X$ of the associated random walk generated by the logarithms of the Perron roots of the mean matrices of this process satisfies the conditions $\mathbf{E}X<0$ and $\mathbf{E}Xe^{X}>0$.

Keywords: multitype branching processes, random environment, survival probability, change of measure.

 Funding Agency Grant Number Russian Science Foundation 17-11-01173

DOI: https://doi.org/10.4213/dm1581

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UDC: 519.218.27

Citation: V. A. Vatutin, E. E. D'yakonova, “Multitype weakly subcritical branching processes in random environment”, Diskr. Mat., 31:3 (2019), 26–46

Citation in format AMSBIB
\Bibitem{VatDya19} \by V.~A.~Vatutin, E.~E.~D'yakonova \paper Multitype weakly subcritical branching processes in random environment \jour Diskr. Mat. \yr 2019 \vol 31 \issue 3 \pages 26--46 \mathnet{http://mi.mathnet.ru/dm1581} \crossref{https://doi.org/10.4213/dm1581}