Geodesic
Asymptotic behaviour of the survival probability of almost critical branching processes in a~random environment
Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 119-140

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A generalization of the well-known result concerning the survival probability of a critical branching process in random environment $Z_k$ is considered. The triangular array scheme of branching processes in random environment $Z_{k,n}$ that are close to $Z_k$ for large $n$ is studied. The equivalence of the survival probabilities for the processes $Z_{n,n}$ and $Z_n$ is obtained under rather natural assumptions on the closeness of $Z_{k,n}$ and $Z_k$. Bibliography: 7 titles.
Keywords: random walks, branching processes, random environments. 
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     author = {V. V. Kharlamov},
     title = {Asymptotic behaviour of the survival probability of almost critical branching processes in a~random environment},
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     number = {1},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_1_a6/}
}
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V. V. Kharlamov. Asymptotic behaviour of the survival probability of almost critical branching processes in a~random environment. Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 119-140. http://geodesic.mathdoc.fr/item/SM_2024_215_1_a6/