Geodesic
Large deviations of branching process in~a~random environment
Diskretnaya Matematika, Tome 31 (2019) no. 4, pp. 102-115

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In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation $Y_{n+1}=A_{n} Y_n + B_n$, where $A_1,A_2,\ldots$ are independent identically distributed random variables and $B_n$ may depend on $\{(A_k,B_k),0\leqslant k$ for any $n\geqslant1$. In the second part of the paper this results are applied to the large deviations of branching processes in a random environment.
Keywords: random difference equations, probabilities of large deviations, branching processes in a random environment } \classification[Funding]{The study was supported by the Russian Science Foundation (project 19-11-00111) in the Steklov Mathematical Institute of Russian Academy of Sciences. 
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     author = {A. V. Shklyaev},
     title = {Large deviations of branching process in~a~random environment},
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A. V. Shklyaev. Large deviations of branching process in~a~random environment. Diskretnaya Matematika, Tome 31 (2019) no. 4, pp. 102-115. http://geodesic.mathdoc.fr/item/DM_2019_31_4_a6/