Avtomat. i Telemekh., 2010, Issue 7, Pages 29–46
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
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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Automation and Remote Control, 2010, 71:7, 1308–1324
Presented by the member of Editorial Board: Б. Г. Волик
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
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\paper Models of branching walks and their use in the reliability theory
\jour Avtomat. i Telemekh.
\jour Autom. Remote Control
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This publication is cited in the following articles:
Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput.
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
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