Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 856-860
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О. V. V'yugin. On transition phenomena in Bellman–Harris branching processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 856-860. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a17/
@article{TVP_1977_22_4_a17,
author = {{\CYRO}. V. V'yugin},
title = {On transition phenomena in {Bellman{\textendash}Harris} branching processes},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {856--860},
year = {1977},
volume = {22},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a17/}
}
TY - JOUR
AU - О. V. V'yugin
TI - On transition phenomena in Bellman–Harris branching processes
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1977
SP - 856
EP - 860
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a17/
LA - ru
ID - TVP_1977_22_4_a17
ER -
%0 Journal Article
%A О. V. V'yugin
%T On transition phenomena in Bellman–Harris branching processes
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1977
%P 856-860
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a17/
%G ru
%F TVP_1977_22_4_a17
Let $\mu(t)=(\mu_1(t),\dots,\mu_r(t))$ be a vector of number of particles in Bellman–Harris branching process with several types of particles. In this article the asymptotic behaviour of the probability $$ \mathbf P\{a^{-1}\otimes\mu(t)\ge x\mid\mu(0)=e_i\},\qquad x>0, $$ when $t\to\infty$, $R\to 1$ in a compact processes class $\mathscr H$, is investigated.
