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Diskr. Mat., 2000, Volume 12, Issue 2, Pages 31–50 (Mi dm326)  

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

On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk

V. I. Afanasyev


Abstract: Let $\{\xi_n\}$ be a critical branching process in a random environment with linear-fractional generating functions, $T$ be the time of extinction of $\{\xi_n\}$, $T_M$ be the first maximum passage time of $\{\xi_n\}$. We study the asymptotic behaviour of $\mathsf P(T_M>n)$ and prove limit theorems for the random variables $\{T_M/n\mid T>n\}$ and $\{T_M/T\mid T>n\}$ as $n\to\infty$. Similar results are established for the stopped random walk with zero drift.

DOI: https://doi.org/10.4213/dm326

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English version:
Discrete Mathematics and Applications, 2000, 10:3, 243–264

Bibliographic databases:

UDC: 519.2
Received: 23.12.1998

Citation: V. I. Afanasyev, “On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk”, Diskr. Mat., 12:2 (2000), 31–50; Discrete Math. Appl., 10:3 (2000), 243–264

Citation in format AMSBIB
\Bibitem{Afa00}
\by V.~I.~Afanasyev
\paper On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 2
\pages 31--50
\mathnet{http://mi.mathnet.ru/dm326}
\crossref{https://doi.org/10.4213/dm326}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1783073}
\zmath{https://zbmath.org/?q=an:0969.60087}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 3
\pages 243--264


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  • http://mi.mathnet.ru/eng/dm/v12/i2/p31

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Afanasyev, “On the ratio between the maximal and total numbers of individuals in a critical branching process in a random environment”, Theory Probab. Appl., 48:3 (2004), 384–399  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. I. Afanasyev, “Functional limit theorem for a stopped random walk attaining a high level”, Discrete Math. Appl., 27:5 (2017), 269–276  mathnet  crossref  crossref  mathscinet  isi  elib
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