Geodesic
The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment
Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 113-128
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We study a multi-type Galton–Watson process in a random environment generated by a sequence of independent identically distributed random variables. For this process we show that under some conditions on the generating functions of offspring distributions the asymptotics of the probability of non-extinction at time $n$ has the order $n^{-1/2}$ as $n\to\infty$.This research was supported by the Russian Foundation for Basic Research, grants 96–01–00338, 96–15–96092, and by INTAS–RFBR, grant 95–0099. 
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     author = {E. E. D'yakonova},
     title = {The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment},
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E. E. D'yakonova. The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment. Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 113-128. http://geodesic.mathdoc.fr/item/DM_1999_11_1_a7/