Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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  - 
%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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a2/
%G ru
%F TVP_1974_19_1_a2
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/