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Diskretnaya Matematika, 2019, Volume 31, Issue 4, Pages 102–115
DOI: https://doi.org/10.4213/dm1575 (Mi dm1575) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Large deviations of branching process in a random environment

A. V. Shklyaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (490 kB) Citations (6)
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DOI: https://doi.org/10.4213/dm1575
Abstract: 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 $\{(A_k,B_k),0\leqslant k<n\}$ 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.
Funding agency Grant number
Russian Science Foundation 19-11-00111
This work was supported by the Russian Science Foundation (project 19-11-00111).
Received: 16.05.2019
Revised: 10.10.2019
English version:
Discrete Mathematics and Applications, 2021, Volume 31, Issue 4, Pages 281–291
DOI: https://doi.org/10.1515/dma-2021-0025
Bibliographic databases:
Document Type: Article
UDC: 519.218.2
Language: Russian
Citation: A. V. Shklyaev, “Large deviations of branching process in a random environment”, Diskr. Mat., 31:4 (2019), 102–115; Discrete Math. Appl., 31:4 (2021), 281–291
Citation in format AMSBIB
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\paper Large deviations of branching process in~a~random environment
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\pages 102--115
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\jour Discrete Math. Appl.
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