Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 638-648
Citer cet article
V. P. Čistyakov. Asymptotic behaviour of the non-extinction probability for a critical Branching process. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 638-648. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/
@article{TVP_1971_16_4_a2,
author = {V. P. \v{C}istyakov},
title = {Asymptotic behaviour of the non-extinction probability for a~critical {Branching} process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {638--648},
year = {1971},
volume = {16},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/}
}
TY - JOUR
AU - V. P. Čistyakov
TI - Asymptotic behaviour of the non-extinction probability for a critical Branching process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 638
EP - 648
VL - 16
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/
LA - ru
ID - TVP_1971_16_4_a2
ER -
%0 Journal Article
%A V. P. Čistyakov
%T Asymptotic behaviour of the non-extinction probability for a critical Branching process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 638-648
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/
%G ru
%F TVP_1971_16_4_a2
Critical age-dependent branching processes with $n$ types $T_1,\dots,T_n$ of particles are considered. Let $\mu_j^i(t)$ be the number of particles of type $T_j$ at time $t$ given that at time $t=0$ there was only one particle of type $T_i$. We derive an asymptotic formula for the probability $\mathbf P\{\mu_1^i(t)+\dots+ \mu_n^i(t)>0\}$ as $t\to\infty$.
