Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 813-825
Citer cet article
M. V. Kozlov. On asymptotics of the probability of nonextinction for a critical branching process in random environment. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 813-825. http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/
@article{TVP_1976_21_4_a9,
author = {M. V. Kozlov},
title = {On asymptotics of the probability of nonextinction for a~critical branching process in random environment},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {813--825},
year = {1976},
volume = {21},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/}
}
TY - JOUR
AU - M. V. Kozlov
TI - On asymptotics of the probability of nonextinction for a critical branching process in random environment
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1976
SP - 813
EP - 825
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/
LA - ru
ID - TVP_1976_21_4_a9
ER -
%0 Journal Article
%A M. V. Kozlov
%T On asymptotics of the probability of nonextinction for a critical branching process in random environment
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1976
%P 813-825
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/
%G ru
%F TVP_1976_21_4_a9
For critical branching processes in random environment, under some slight restrictions, the following inequalities for the tails of the extinction time distribution are proved: \begin{equation} c_1/\sqrt n\le\mathbf P(T>n)\le c_2/\sqrt n. \end{equation} In the case of fractional linear generating functions, (1) is replaced by $$ \mathbf P(T>n)\sim c/\sqrt n,\qquad n\to\infty. $$
