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
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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 $n\to\infty$.
@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},
publisher = {mathdoc},
volume = {19},
number = {1},
year = {1974},
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 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/ LA - ru ID - TVP_1974_19_1_a2 ER -
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/