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.
@article{DM_1999_11_1_a7,
author = {E. E. D'yakonova},
title = {The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment},
journal = {Diskretnaya Matematika},
pages = {113--128},
publisher = {mathdoc},
volume = {11},
number = {1},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1999_11_1_a7/}
}
TY - JOUR AU - E. E. D'yakonova TI - The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment JO - Diskretnaya Matematika PY - 1999 SP - 113 EP - 128 VL - 11 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DM_1999_11_1_a7/ LA - ru ID - DM_1999_11_1_a7 ER -
%0 Journal Article %A E. E. D'yakonova %T The asymptotics of the probability of nonextinction of a multidimensional branching process in a random environment %J Diskretnaya Matematika %D 1999 %P 113-128 %V 11 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DM_1999_11_1_a7/ %G ru %F DM_1999_11_1_a7
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/