Geodesic
On asymptotics of the probability of nonextinction for a critical branching process in random environment
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 813-825 Cet article a éte moissonné depuis la source Math-Net.Ru

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For critical branching processes in random environment, under some slight restrictions, the following inequalities for the tails of the extinction time distribution are proved: \begin{equation} c_1/\sqrt n\le\mathbf P(T>n)\le c_2/\sqrt n. \end{equation} In the case of fractional linear generating functions, (1) is replaced by $$ \mathbf P(T>n)\sim c/\sqrt n,\qquad n\to\infty. $$ 
@article{TVP_1976_21_4_a9,
     author = {M. V. Kozlov},
     title = {On asymptotics of the probability of nonextinction for a~critical branching process in random environment},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {813--825},
     year = {1976},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/}
}
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M. V. Kozlov. On asymptotics of the probability of nonextinction for a critical branching process in random environment. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 813-825. http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a9/