Geodesic
Critical multitype branching processes in a~random environment
Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 23-41

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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 associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices satisfies Spitzer's condition, we find the asymptotics of the survival probability at time $n$ as $n\to\infty$. 
@article{DM_2007_19_4_a1,
     author = {E. E. D'yakonova},
     title = {Critical multitype branching processes in a~random environment},
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     number = {4},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2007_19_4_a1/}
}
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E. E. D'yakonova. Critical multitype branching processes in a~random environment. Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 23-41. http://geodesic.mathdoc.fr/item/DM_2007_19_4_a1/