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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 3, Pages 435–452 (Mi tvp264)  

This article is cited in 2 scientific papers (total in 2 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

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.

DOI: https://doi.org/10.4213/tvp264

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English version:
Theory of Probability and its Applications, 2004, 48:3, 384–399

Bibliographic databases:

Received: 04.02.2002

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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\jour Theory Probab. Appl.
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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. M. V. Kozlov, “On large deviations of branching processes in a random environment: a geometric distribution of the number of descendants”, Discrete Math. Appl., 16:2 (2006), 155–174  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. V. I. Afanasyev, “On the time of attaining a high level by a transient random walk in a random environment”, Theory Probab. Appl., 61:2 (2017), 178–207  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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