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 Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 2, Pages 283–307 (Mi tvp5243)

Branching random walks on $\mathbf{Z}^d$ with periodic branching sources

M. V. Platonovaab, K. S. Ryadovkinc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
c Saint Petersburg State University

Abstract: We consider a continuous-time branching random walk on $\mathbf{Z}^d$ with birth and death of particles at a periodic set of points (the sources of branching). Spectral properties of the evolution operator of the mean number of particles at an arbitrary point of the lattice are studied. The leading term of the asymptotics as $t\to\infty$ of the mean number of particles at a given point is obtained. Under an additional moment condition, an asymptotic series expansion of the mean number of particles is derived.

Keywords: branching random walk, periodic perturbation, evolution equation.

 Funding Agency Grant Number Russian Science Foundation 17-11-01136 This research was carried out with the financial support of the Russian Science Foundation (grant 17-11-01136).

DOI: https://doi.org/10.4213/tvp5243

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English version:
Theory of Probability and its Applications, 2019, 64:2, 229–248

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Revised: 17.07.2018
Accepted:29.08.2018

Citation: M. V. Platonova, K. S. Ryadovkin, “Branching random walks on $\mathbf{Z}^d$ with periodic branching sources”, Teor. Veroyatnost. i Primenen., 64:2 (2019), 283–307; Theory Probab. Appl., 64:2 (2019), 229–248

Citation in format AMSBIB
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