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Avtomat. i Telemekh., 2010, Issue 7, Pages 29–46 (Mi at845)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Models and Methods of Reliability Theory

Models of branching walks and their use in the reliability theory

E. B. Yarovaya

M. V. Lomonosov Moscow State University

Abstract: Application of the branching walk models in the reliability theory was discussed. The results obtained for the models of a symmetric continuous-time branching random walk on $\mathbf Z^d$ with the source of particle birth and death at one of the lattice points were reviewed. Emphasis was made on the survival analysis and study of the branching walk properties depending on the source intensity. It was shown that if $d\ge3$, then under the supercritical branching process at the source the supercritical, critical and even subcritical branching random walk may arise on $\mathbf Z^d$. A classification relying on the asymptotic behavior of the number of particles at an arbitrary lattice point which specifies the phase transitions on lattice dimension for the critical and subcritical branching random walk was presented.

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English version:
Automation and Remote Control, 2010, 71:7, 1308–1324

Bibliographic databases:

Presented by the member of Editorial Board: Б. Г. Волик

Received: 20.08.2009

Citation: E. B. Yarovaya, “Models of branching walks and their use in the reliability theory”, Avtomat. i Telemekh., 2010, no. 7, 29–46; Autom. Remote Control, 71:7 (2010), 1308–1324

Citation in format AMSBIB
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\paper Models of branching walks and their use in the reliability theory
\jour Avtomat. i Telemekh.
\yr 2010
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\pages 29--46
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\transl
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\vol 71
\issue 7
\pages 1308--1324
\crossref{https://doi.org/10.1134/S0005117910070052}
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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. Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput.  crossref  isi
    2. E. B. Yarovaya, “Criterions of the exponential growth of particles for some models of branching random walks”, Theory Probab. Appl., 55:4 (2011), 661–682  mathnet  crossref  crossref  mathscinet  isi
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