Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 100-126
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V. A. Vatutin; E. E. D'yakonova. Critical branching processes in random environment: the probability of extinction at a given moment. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 100-126. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a10/
@article{DM_1997_9_4_a10,
author = {V. A. Vatutin and E. E. D'yakonova},
title = {Critical branching processes in random environment: the probability of extinction at a given moment},
journal = {Diskretnaya Matematika},
pages = {100--126},
year = {1997},
volume = {9},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a10/}
}
TY - JOUR
AU - V. A. Vatutin
AU - E. E. D'yakonova
TI - Critical branching processes in random environment: the probability of extinction at a given moment
JO - Diskretnaya Matematika
PY - 1997
SP - 100
EP - 126
VL - 9
IS - 4
UR - http://geodesic.mathdoc.fr/item/DM_1997_9_4_a10/
LA - ru
ID - DM_1997_9_4_a10
ER -
%0 Journal Article
%A V. A. Vatutin
%A E. E. D'yakonova
%T Critical branching processes in random environment: the probability of extinction at a given moment
%J Diskretnaya Matematika
%D 1997
%P 100-126
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/DM_1997_9_4_a10/
%G ru
%F DM_1997_9_4_a10
Let $\kappa$ be the extinction moment of a critical branching process in random environment with linear-fractional generating functions $f_n(s)$ of the number of particles in the $n$th generation, $n=1,2,\dots$ We give conditions on the parameters of $f_n(s)$ under which $$ \mathsf P\{\kappa=n\}\sim cn^{-3/2}, $$ as $n\to\infty$, where $c$ is a positive constant. This research was supported by the Russian Foundation for Basic Research, grant 96–01–00338, and by INTAS–RFBR, grant 95–0099.
