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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 2, Pages 231–268
DOI: https://doi.org/10.4213/tvp218 (Mi tvp218) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Galton–Watson branching processes in a random environment. II: Finite-dimensional distributions

V. A. Vatutin, E. E. D'yakonova

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (3099 kB) Citations (24)
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DOI: https://doi.org/10.4213/tvp218
Abstract: Let $Z_n$ be the number of particles at moment $n$ in a branching process in a random environment. Assuming that $Z_n$ is “critical” in a certain sense we prove theorems describing the asymptotic behavior as $n\to\infty$ of the distribution of the vector $(Z_{[nt_1]},\dots,Z_{[nt_{b}]})$, of the number of particles in the process at moments $0<[nt_1]<\dots<[nt_{b}]=n$ given $ Z_n>0$.
Keywords: branching processes in random environment, survival probability, limit theorems, critical branching process, random walks, Spitzer condition, stable distributions, joint distributions.
Received: 17.03.2004
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 2, Pages 275–309
DOI: https://doi.org/10.1137/S0040585X97981007
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Vatutin, E. E. D'yakonova, “Galton–Watson branching processes in a random environment. II: Finite-dimensional distributions”, Teor. Veroyatnost. i Primenen., 49:2 (2004), 231–268; Theory Probab. Appl., 49:2 (2005), 275–309
Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 2
\pages 275--309
\crossref{https://doi.org/10.1137/S0040585X97981007}
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  • https://www.mathnet.ru/eng/tvp/v49/i2/p231
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    This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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