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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 3, Pages 435–452
DOI: https://doi.org/10.4213/tvp264
(Mi tvp264)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the ratio between the maximal and total numbers of individuals in a critical branching process in a random environment

V. I. Afanasyev

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: Let $\{\xi_n\}$ be a critical branching process in a random environment. Under some restrictions on the characteristics of the process, we show that the ratio of $\sum_{i=0}^n\xi_i$ to $\max_{0\leqq i\leqq n}\xi_i$, given $\{\xi_n>0\}$, converges in distribution as $n\to\infty$ to a random variable taking on values in $(1,+\infty)$.
Keywords: branching process in a random environment, conditional random walk, conditional limit theorems.
Received: 04.02.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 3, Pages 384–399
DOI: https://doi.org/10.1137/S0040585X97980506
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Afanasyev, “On the ratio between the maximal and total numbers of individuals in a critical branching process in a random environment”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 435–452; Theory Probab. Appl., 48:3 (2004), 384–399
Citation in format AMSBIB
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\pages 435--452
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 384--399
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Linking options:
  • https://www.mathnet.ru/eng/tvp264
  • https://doi.org/10.4213/tvp264
  • https://www.mathnet.ru/eng/tvp/v48/i3/p435
  • This publication is cited in the following 3 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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    References:58
     
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