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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 3, Pages 456–480
DOI: https://doi.org/10.4213/tvp5245
(Mi tvp5245)
 

This article is cited in 13 scientific papers (total in 14 papers)

A limit theorem for supercritical random branching walks with branching sources of varying intensity

I. Khristolyubov, E. B. Yarovaya

Lomonosov Moscow State University
References:
Abstract: We consider a supercritical symmetric continuous-time branching random walk on a multidimensional lattice with a finite number of particle generation sources of varying positive intensities without any restrictions on the variance of jumps of the underlying random walk. It is assumed that the spectrum of the evolution operator contains at least one positive eigenvalue. We prove that under these conditions the largest eigenvalue of the evolution operator is simple and determines the rate of exponential growth of particle quantities at each point on the lattice as well as on the lattice as a whole.
Keywords: branching random walk, multiple sources, supercritical case, limit theorem, particle number exponential growth.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00468
This research was carried out with the financial support of the Russian Foundation for Basic Research (project no. 17-01-00468).
Received: 21.08.2018
Revised: 27.12.2018
Accepted: 24.01.2019
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 3, Pages 365–384
DOI: https://doi.org/10.1137/S0040585X97T989556
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. Khristolyubov, E. B. Yarovaya, “A limit theorem for supercritical random branching walks with branching sources of varying intensity”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 456–480; Theory Probab. Appl., 64:3 (2019), 365–384
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v64/i3/p456
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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