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Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 3, Pages 456–480 (Mi tvp5245)  

This article is cited in 2 scientific papers (total in 3 papers)

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

I. Khristolyubov, E. B. Yarovaya

Lomonosov Moscow State University

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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tvp5245

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English version:
Theory of Probability and its Applications, 2019, 64:3, 365–384

Bibliographic databases:

MSC: 60J35 60J80 60B99
Received: 21.08.2018
Revised: 27.12.2018
Accepted:24.01.2019

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Rytova, E. B. Yarovaya, “Moments of the numbers of particles in a heavy-tailed branching random walk”, Russian Math. Surveys, 74:6 (2019), 1126–1128  mathnet  crossref  crossref  isi
    2. E. B. Yarovaya, J. Stoyanov, K. K. Kostyashin, “On conditions for a probability distribution to be uniquely determined by its moments”, Theory Probab. Appl., 64:4 (2019), 579–594  mathnet  crossref  crossref
    3. “Tezisy dokladov, predstavlennykh na Chetvertoi mezhdunarodnoi konferentsii po stokhasticheskim metodam”, Teoriya veroyatn. i ee primen., 65:1 (2020), 151–210  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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