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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 3, Pages 449–464 (Mi tvp33)  

This article is cited in 5 scientific papers (total in 5 papers)

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

V. I. Afanasyev

Steklov Mathematical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/tvp33

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English version:
Theory of Probability and its Applications, 2007, 51:3, 401–414

Bibliographic databases:

Received: 28.12.2004
Revised: 23.11.2005

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Afanasyev, “Invariance Principle for the Critical Branching Process in a Random Environment Attaining a High Level”, Theory Probab. Appl., 54:1 (2010), 1–13  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. I. Afanasyev, “Brownian high jump”, Theory Probab. Appl., 55:2 (2011), 183–197  mathnet  crossref  crossref  mathscinet  isi
    3. Afanasyev V.I., “New invariance principles for critical branching process in random environment”, Advances in data analysis, Stat. Ind. Technol., Birkhäuser Boston, Boston, MA, 2010, 105–115  mathscinet  isi
    4. V. I. Afanasyev, “High level subcritical branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 4–14  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. V. I. Afanasyev, “Functional limit theorem for a stopped random walk attaining a high level”, Discrete Math. Appl., 27:5 (2017), 269–276  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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