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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 3, Pages 449–464
DOI: https://doi.org/10.4213/tvp33 (Mi tvp33) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Arcsine law for branching processes in a random environment and Galton–Watson processes

V. I. Afanasyev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (1258 kB) Citations (7)
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DOI: https://doi.org/10.4213/tvp33
Abstract: Two closely related results are established. A given critical branching process in a random environment attains a high level and spends at that level a part of its life obeying the arcsine law. If a critical Galton–Watson process survives up to a distant moment, then the ratio of the total number of individuals of the future generations to the total number of individuals ever born in the process obeys the arcsine law.
Keywords: branching process in a random environment, Galton–Watson process, stopped random walk, conditional invariance principle, conditional limit theorems, arcsine law.
Received: 28.12.2004
Revised: 23.11.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 3, Pages 401–414
DOI: https://doi.org/10.1137/S0040585X97982463
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Afanasyev, “Arcsine law for branching processes in a random environment and Galton–Watson processes”, Teor. Veroyatnost. i Primenen., 51:3 (2006), 449–464; Theory Probab. Appl., 51:3 (2007), 401–414
Citation in format AMSBIB
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    • This publication is cited in the following 7 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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