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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 3, Pages 453–465
DOI: https://doi.org/10.4213/tvp265 (Mi tvp265) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Limit theorem for an intermediate subcritical branching process in a random environment

V. A. Vatutin

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (1378 kB) Citations (14)
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DOI: https://doi.org/10.4213/tvp265
Abstract: The asymptotic behavior of the survival probability of an intermediate subcritical branching process $Z_n$ in a random environment is found when a transformation of the reproduction law of the offspring number is attracted to a stable law $\alpha\in (1,2]$. It is shown that the distribution of the random variable $\{Z_n\}$ given $Z_n>0$ converges to a nondegenerate distribution as $n\to\infty$.
Keywords: branching processes in a random environment, survival probability, intermediate subcritical process, limit theorem, random walks, stable distributions.
Received: 03.12.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 3, Pages 481–492
DOI: https://doi.org/10.1137/S0040585X97980518
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Vatutin, “Limit theorem for an intermediate subcritical branching process in a random environment”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 453–465; Theory Probab. Appl., 48:3 (2004), 481–492
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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\issue 3
\pages 481--492
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  • https://doi.org/10.4213/tvp265
  • https://www.mathnet.ru/eng/tvp/v48/i3/p453
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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