Geodesic
Multitype subcritical branching processes in a~random environment
Informatics and Automation, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 87-97

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We investigate a multitype Galton–Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment $X$ of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable $Xe^X$ has zero mean, we find the asymptotics of the survival probability at time $n$ as $n\to\infty$. 
@article{TRSPY_2013_282_a7,
     author = {E. E. Dyakonova},
     title = {Multitype subcritical branching processes in a~random environment},
     journal = {Informatics and Automation},
     pages = {87--97},
     publisher = {mathdoc},
     volume = {282},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a7/}
}
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E. E. Dyakonova. Multitype subcritical branching processes in a~random environment. Informatics and Automation, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 87-97. http://geodesic.mathdoc.fr/item/TRSPY_2013_282_a7/