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Diskretnaya Matematika, 2022, Volume 34, Issue 3, Pages 3–19
DOI: https://doi.org/10.4213/dm1724
(Mi dm1724)
 

This article is cited in 2 scientific papers (total in 2 papers)

Weakly supercritical branching process in unfavourable environment

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (495 kB) Citations (2)
References:
Abstract: Let $\{Z_{n}\}$ be a weakly supercritical branching process in a random environment, and $\{S_{n}\}$ be its associated random walk. We consider a natural martingale $W_{n}=Z_{n}\exp(-S_{n})$, where $n\geq 0$. We prove two limit theorems for the random process $W_{\lfloor nt\rfloor}$, where $t\in [0,1]$, which is considered either under the condition on the unfavourable environment $\{\max_{1\leq i\leq n}S_{i}\}$ or under the condition on the unfavourable environment $\{S_{n}\leq u\}$, where $u$ is some positive constant.
Keywords: weakly supercritical branching process in a random environment, conditional functional limit theorems
Funding agency Grant number
Russian Science Foundation 19-11-00111
Received: 27.05.2022
English version:
Discrete Mathematics and Applications, 2024, Volume 34, Issue 1, Pages 1–13
DOI: https://doi.org/10.1515/dma-2024-0001
Bibliographic databases:
Document Type: Article
UDC: 519.218.27
Language: Russian
Citation: V. I. Afanasyev, “Weakly supercritical branching process in unfavourable environment”, Diskr. Mat., 34:3 (2022), 3–19; Discrete Math. Appl., 34:1 (2024), 1–13
Citation in format AMSBIB
\Bibitem{Afa22}
\by V.~I.~Afanasyev
\paper Weakly supercritical branching process in unfavourable environment
\jour Diskr. Mat.
\yr 2022
\vol 34
\issue 3
\pages 3--19
\mathnet{http://mi.mathnet.ru/dm1724}
\crossref{https://doi.org/10.4213/dm1724}
\transl
\jour Discrete Math. Appl.
\yr 2024
\vol 34
\issue 1
\pages 1--13
\crossref{https://doi.org/10.1515/dma-2024-0001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001163652600002}
Linking options:
  • https://www.mathnet.ru/eng/dm1724
  • https://doi.org/10.4213/dm1724
  • https://www.mathnet.ru/eng/dm/v34/i3/p3
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Abstract page:300
    Full-text PDF :39
    References:46
    First page:11
     
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