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Diskr. Mat., 2005, Volume 17, Issue 1, Pages 35–49 (Mi dm86)  

This article is cited in 3 scientific papers (total in 3 papers)

On a conditional invariance principle for a critical Galton–Watson branching process

V. I. Afanasyev


Abstract: For a critical Galton–Watson branching process, we formulate an invariance principle which allows us to study the process in two time scales, absolute and relative (to the life time of the process). We establish a relation between the limiting process and the local time of the Brownian excursion.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–00266, and by the program of the President of Russian Federation of supporting leading scientific schools, grant 1758.2003.1.

DOI: https://doi.org/10.4213/dm86

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English version:
Discrete Mathematics and Applications, 2005, 15:1, 17–32

Bibliographic databases:

UDC: 519.2
Received: 20.01.2004
Revised: 12.10.2004

Citation: V. I. Afanasyev, “On a conditional invariance principle for a critical Galton–Watson branching process”, Diskr. Mat., 17:1 (2005), 35–49; Discrete Math. Appl., 15:1 (2005), 17–32

Citation in format AMSBIB
\Bibitem{Afa05}
\by V.~I.~Afanasyev
\paper On a conditional invariance principle for a critical Galton--Watson branching process
\jour Diskr. Mat.
\yr 2005
\vol 17
\issue 1
\pages 35--49
\mathnet{http://mi.mathnet.ru/dm86}
\crossref{https://doi.org/10.4213/dm86}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2164522}
\zmath{https://zbmath.org/?q=an:1113.60088}
\elib{https://elibrary.ru/item.asp?id=9135411}
\transl
\jour Discrete Math. Appl.
\yr 2005
\vol 15
\issue 1
\pages 17--32
\crossref{https://doi.org/10.1515/1569392053310382}


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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, “Arcsine law for branching processes in a random environment and Galton–Watson processes”, Theory Probab. Appl., 51:3 (2007), 401–414  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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
  • Дискретная математика
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