Geodesic
Asymptotic behaviour of the non-extinction probability for a~critical Branching process
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 638-648

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Critical age-dependent branching processes with $n$ types $T_1,\dots,T_n$ of particles are considered. Let $\mu_j^i(t)$ be the number of particles of type $T_j$ at time $t$ given that at time $t=0$ there was only one particle of type $T_i$. We derive an asymptotic formula for the probability $\mathbf P\{\mu_1^i(t)+\dots+ \mu_n^i(t)>0\}$ as $t\to\infty$. 
@article{TVP_1971_16_4_a2,
     author = {V. P. \v{C}istyakov},
     title = {Asymptotic behaviour of the non-extinction probability for a~critical {Branching} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {638--648},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/}
}
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V. P. Čistyakov. Asymptotic behaviour of the non-extinction probability for a~critical Branching process. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 638-648. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a2/