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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 234–256 (Mi znsl6552)  

Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching

M. V. Platonovaab, K. S. Ryadovkinc

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

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 an evolution operator of the mean number of particles are studied. We derive a representation of the mean value of particle number in a form of asymptotic series.

Key words and phrases: branching random walk, periodic perturbation, evolution equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00443а
16-01-00087
Möbius Contest


Full text: PDF file (267 kB)
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Document Type: Article
UDC: 519.21
Received: 23.10.2017

Citation: M. V. Platonova, K. S. Ryadovkin, “Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 234–256

Citation in format AMSBIB
\Bibitem{PlaRya17}
\by M.~V.~Platonova, K.~S.~Ryadovkin
\paper Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 234--256
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6552}


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