Geodesic
Multitype weakly subcritical branching processes in random environment
Diskretnaya Matematika, Tome 31 (2019) no. 3, pp. 26-46.

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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 $\mathbf{E}X0$ and $\mathbf{E}Xe^{X}>0$.
Keywords: multitype branching processes, random environment, survival probability, change of measure. 
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V. A. Vatutin; E. E. D'yakonova. Multitype weakly subcritical branching processes in random environment. Diskretnaya Matematika, Tome 31 (2019) no. 3, pp. 26-46. http://geodesic.mathdoc.fr/item/DM_2019_31_3_a2/

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