Geodesic
Limit theorem for an intermediate subcritical branching process in a
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 453-465

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The asymptotic behavior of the survival probability of an intermediate subcritical branching process $Z_n$ in a random environment is found when a transformation of the reproduction law of the offspring number is attracted to a stable law $\alpha\in (1,2]$. It is shown that the distribution of the random variable $\{Z_n\}$ given $Z_n>0$ converges to a nondegenerate distribution as $n\to\infty$.
Keywords: branching processes in a random environment, survival probability, intermediate subcritical process, limit theorem, random walks
Mots-clés : stable distributions. 
@article{TVP_2003_48_3_a1,
     author = {V. A. Vatutin},
     title = {Limit theorem for an intermediate subcritical branching process in a},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {453--465},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a1/}
}
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V. A. Vatutin. Limit theorem for an intermediate subcritical branching process in a. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 453-465. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a1/