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Teor. Veroyatnost. i Primenen., 2009, Volume 54, Issue 1, Pages 3–17 (Mi tvp2496)  

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

Invariance Principle for the Critical Branching Process in a Random Environment Attaining a High Level

V. I. Afanasyev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A conditional invariance principle is established for the critical branching process in a random environment attaining a high level, and finite-dimensional distributions of the limiting process are found.

Keywords: branching process in a random environment, conditional invariance principles, Brownian excursion, Brownian meander

DOI: https://doi.org/10.4213/tvp2496

Full text: PDF file (186 kB)
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English version:
Theory of Probability and its Applications, 2010, 54:1, 1–13

Bibliographic databases:

Received: 14.12.2007
Revised: 20.06.2008

Citation: V. I. Afanasyev, “Invariance Principle for the Critical Branching Process in a Random Environment Attaining a High Level”, Teor. Veroyatnost. i Primenen., 54:1 (2009), 3–17; Theory Probab. Appl., 54:1 (2010), 1–13

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, “Brownian high jump”, Theory Probab. Appl., 55:2 (2011), 183–197  mathnet  crossref  crossref  mathscinet  isi
    2. 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
    3. V. I. Afanasyev, “Functional limit theorems for high-level subcritical branching processes in random environment”, Discrete Math. Appl., 24:5 (2014), 257–272  mathnet  crossref  crossref  mathscinet  elib
    4. Bansaye V., Simatos F., “on the Scaling Limits of Galton-Watson Processes in Varying Environments”, Electron. J. Probab., 20 (2015), 75  crossref  mathscinet  zmath  isi  elib  scopus
    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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