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Teoriya Veroyatnostei i ee Primeneniya, 1997, Volume 42, Issue 1, Pages 21–34
DOI: https://doi.org/10.4213/tvp1709 (Mi tvp1709) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Maximum of the critical Galton–Watson processes and left-continuous random walks

V. A. Vatutina, V. A. Topchiib

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Information Technologies and Applied Mathematics
Full-text PDF (540 kB) Citations (20)
DOI: https://doi.org/10.4213/tvp1709
Abstract: Let $Z(n)$, $n=0,1,\dots$ be a critical Galton–Watson branching process, $Z(0)=1$. Under mild conditions on the distribution of $Z(1)$, we prove that
$$ \mathsf{E}\max_{1\le k\le n}Z(k)\sim\log n, \qquad n\to\infty. $$
Keywords: critical branching process, maximum of a branching process, the von Bahr–Esseen inequality, left-continuous random walk.
Received: 11.04.1996
English version:
Theory of Probability and its Applications, 1998, Volume 42, Issue 1, Pages 17–27
DOI: https://doi.org/10.1137/S0040585X97975903
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Vatutin, V. A. Topchii, “Maximum of the critical Galton–Watson processes and left-continuous random walks”, Teor. Veroyatnost. i Primenen., 42:1 (1997), 21–34; Theory Probab. Appl., 42:1 (1998), 17–27
Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 1
\pages 17--27
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  • https://www.mathnet.ru/eng/tvp/v42/i1/p21
    • This publication is cited in the following 20 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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