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Diskr. Mat., 1997, Volume 9, Issue 4, Pages 100–126 (Mi dm505)  

This article is cited in 5 scientific papers (total in 5 papers)

Critical branching processes in random environment: the probability of extinction at a given moment

V. A. Vatutin, E. E. D'yakonova


Abstract: Let $\kappa$ be the extinction moment of a critical branching process in random environment with linear-fractional generating functions $f_n(s)$ of the number of particles in the $n$th generation, $n=1,2,…$ We give conditions on the parameters of $f_n(s)$ under which
$$ \mathsf P\{\kappa=n\}\sim cn^{-3/2}, $$
as $n\to\infty$, where $c$ is a positive constant.
This research was supported by the Russian Foundation for Basic Research, grant 96–01–00338, and by INTAS–RFBR, grant 95–0099.

DOI: https://doi.org/10.4213/dm505

Full text: PDF file (1795 kB)

English version:
Discrete Mathematics and Applications, 1997, 7:5, 469–496

Bibliographic databases:

UDC: 519.2
Received: 28.06.1996

Citation: V. A. Vatutin, E. E. D'yakonova, “Critical branching processes in random environment: the probability of extinction at a given moment”, Diskr. Mat., 9:4 (1997), 100–126; Discrete Math. Appl., 7:5 (1997), 469–496

Citation in format AMSBIB
\Bibitem{VatDya97}
\by V.~A.~Vatutin, E.~E.~D'yakonova
\paper Critical branching processes in random environment: the probability of extinction at a given moment
\jour Diskr. Mat.
\yr 1997
\vol 9
\issue 4
\pages 100--126
\mathnet{http://mi.mathnet.ru/dm505}
\crossref{https://doi.org/10.4213/dm505}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629616}
\zmath{https://zbmath.org/?q=an:0977.60088}
\transl
\jour Discrete Math. Appl.
\yr 1997
\vol 7
\issue 5
\pages 469--496


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fleischmann K., Vatutin V.A., “Reduced subcritical Galton-Watson processes in a random environment”, Advances in Applied Probability, 31:1 (1999), 88–111  crossref  mathscinet  zmath  isi  scopus
    2. V. A. Vatutin, E. E. D'yakonova, “Galton–Watson branching processes in a random environment. I: limit theorems”, Theory Probab. Appl., 48:2 (2004), 314–336  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. A. Vatutin, V. I. Vakhtel', “Sudden extinction of the critical branching process in random environment”, Theory Probab. Appl., 54:3 (2010), 466–484  mathnet  crossref  crossref  mathscinet  isi
    4. V. A. Vatutin, “Total Population Size in Critical Branching Processes in a Random Environment”, Math. Notes, 91:1 (2012), 12–21  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. V. A. Vatutin, E. E. Dyakonova, S. Sagitov, “Evolution of branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 220–242  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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