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Mat. Zametki, 2011, Volume 90, Issue 6, Pages 845–859 (Mi mz8863)  

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

Limit Distributions for the Number of Particles in Branching Random Walks

E. Vl. Bulinskaya

M. V. Lomonosov Moscow State University

Abstract: We study branching random walks with continuous time. Particles performing a random walk on $\mathbb{Z}^{2}$, are allowed to be born and die only at the origin. It is assumed that the offspring reproduction law at the branching source is critical and the random walk outside the source is homogeneous and symmetric. Given particles at the origin, we prove a conditional limit theorem for the joint distribution of suitably normalized numbers of particles at the source and outside it as time unboundedly increases. As a consequence, we establish the asymptotic independence of such random variables.

Keywords: branching random walk, branching source, offspring reproduction law, Bellman–Harris branching process, probability generating function, transition rate matrix

DOI: https://doi.org/10.4213/mzm8863

Full text: PDF file (534 kB)
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English version:
Mathematical Notes, 2011, 90:6, 824–837

Bibliographic databases:

UDC: 519.21
Received: 27.08.2010
Revised: 27.12.2010

Citation: E. Vl. Bulinskaya, “Limit Distributions for the Number of Particles in Branching Random Walks”, Mat. Zametki, 90:6 (2011), 845–859; Math. Notes, 90:6 (2011), 824–837

Citation in format AMSBIB
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\by E.~Vl.~Bulinskaya
\paper Limit Distributions for the Number of Particles in Branching Random Walks
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 6
\pages 845--859
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\crossref{https://doi.org/10.4213/mzm8863}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962960}
\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 6
\pages 824--837
\crossref{https://doi.org/10.1134/S0001434611110228}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855180581}


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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. A. Vatutin, V. A. Topchii, “Critical Bellman–Harris branching processes with long-living particles”, Proc. Steklov Inst. Math., 282 (2013), 243–272  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. E. Vl. Bulinskaya, “Subcritical catalytic branching random walk with finite or infinite variance of offspring number”, Proc. Steklov Inst. Math., 282 (2013), 62–72  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. E. V. Bulinskaya, “Local particles numbers in critical branching random walk”, J. Theor. Probab., 27:3 (2014), 878–898  crossref  mathscinet  zmath  isi  scopus
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