Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 26-35
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V. A. Vatutin. The asymptotic probability of the first degeneration for branching processes with immigration. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 26-35. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/
@article{TVP_1974_19_1_a2,
author = {V. A. Vatutin},
title = {The asymptotic probability of the first degeneration for branching processes with immigration},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {26--35},
year = {1974},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/}
}
TY - JOUR
AU - V. A. Vatutin
TI - The asymptotic probability of the first degeneration for branching processes with immigration
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 26
EP - 35
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/
LA - ru
ID - TVP_1974_19_1_a2
ER -
%0 Journal Article
%A V. A. Vatutin
%T The asymptotic probability of the first degeneration for branching processes with immigration
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 26-35
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/
%G ru
%F TVP_1974_19_1_a2
Let $\eta(t)$ be the number of particles in a branching process with immigration at time $t$. The initial lifeperiod of the branching process with immigration equals $\tau$ if $\eta(0)=n>0$, $\eta(t)>0$ for all $t\in(0,\tau)$ and $\eta(\tau)=0$ (sample paths of the process, are supposed to be right continuous). We obtain asymptotic formulas for $Q_n=\mathbf P\{\tau<\infty\mid\eta(0)=n\}$ as $n\to\infty$.
