Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 348-354
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B. I. Selivanov. Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 348-354. http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a16/
@article{TVP_1969_14_2_a16,
author = {B. I. Selivanov},
title = {Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {348--354},
year = {1969},
volume = {14},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a16/}
}
TY - JOUR
AU - B. I. Selivanov
TI - Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 348
EP - 354
VL - 14
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a16/
LA - ru
ID - TVP_1969_14_2_a16
ER -
%0 Journal Article
%A B. I. Selivanov
%T Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 348-354
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a16/
%G ru
%F TVP_1969_14_2_a16
Let $Z_0=1$, $Z_n$, $n=1,2,\dots,$ be the number of particles belonging to the $n$-th generation of a Halton–Watson branching process, $p_{nr}=\mathbf P\{Z_n=r\}$ and $F_n(z)=\sum_{r\ge0}p_{nr}z^r$. It is supposed that $m=\mathbf EZ_1\ne1$ and $F(z)=F_1(z)$ be regular at the point $z=1$ for $m<1$. In the paper some formulas and an asymptotic expansion for the probabilities $p_{nr}$ are obtained.
