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Diskr. Mat., 1998, Volume 10, Issue 3, Pages 131–147 (Mi dm429)  

This article is cited in 1 scientific paper (total in 2 paper)

A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment

V. I. Afanasyev


Abstract: Let $\{\xi_n\}$ be a moderately subcritical branching process in a random environment with linear-fractional generating functions. We prove that, as $n\to\infty$, the sequence of stochastic processes $\{\ln\xi_{[nt]}/(\Delta \sqrt n), t\in [0,1]\mid \xi_n>0\}$, where $\Delta$ is some positive constant, converges in distribution to the Brownian excursion $\{W_0^+(t), t\in [0,1]\}$ in the space $D[0,1]$ with Skorokhod topology.

DOI: https://doi.org/10.4213/dm429

Full text: PDF file (1193 kB)

English version:
Discrete Mathematics and Applications, 1998, 8:4, 421–438

Bibliographic databases:

UDC: 519.2
Received: 19.12.1997

Citation: V. I. Afanasyev, “A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment”, Diskr. Mat., 10:3 (1998), 131–147; Discrete Math. Appl., 8:4 (1998), 421–438

Citation in format AMSBIB
\Bibitem{Afa98}
\by V.~I.~Afanasyev
\paper A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment
\jour Diskr. Mat.
\yr 1998
\vol 10
\issue 3
\pages 131--147
\mathnet{http://mi.mathnet.ru/dm429}
\crossref{https://doi.org/10.4213/dm429}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1673686}
\zmath{https://zbmath.org/?q=an:1002.60528}
\transl
\jour Discrete Math. Appl.
\yr 1998
\vol 8
\issue 4
\pages 421--438


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  • http://mi.mathnet.ru/eng/dm/v10/i3/p131

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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. V. A. Vatutin, E. E. D'yakonova, “Multitype weakly subcritical branching processes in random environment”, Discrete Math. Appl., 31:3 (2021), 207–222  mathnet  crossref  crossref  mathscinet  isi  elib
    2. “Abstracts of talks given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172  mathnet  crossref  crossref  isi  elib
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