RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (568 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

MSC: 60J35 60J80 60B99
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
\Bibitem{KhrYar19} \by I.~Khristolyubov, E.~B.~Yarovaya \paper A limit theorem for supercritical random branching walks with branching sources of varying intensity \jour Teor. Veroyatnost. i Primenen. \yr 2019 \vol 64 \issue 3 \pages 456--480 \mathnet{http://mi.mathnet.ru/tvp5245} \crossref{https://doi.org/10.4213/tvp5245} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3988269} \zmath{https://zbmath.org/?q=an:07122183} \elib{http://elibrary.ru/item.asp?id=38590353} \transl \jour Theory Probab. Appl. \yr 2019 \vol 64 \issue 3 \pages 365--384 \crossref{https://doi.org/10.1137/S0040585X97T989556} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000492370500003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074324983} 

• http://mi.mathnet.ru/eng/tvp5245
• https://doi.org/10.4213/tvp5245
• http://mi.mathnet.ru/eng/tvp/v64/i3/p456

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
3. “Tezisy dokladov, predstavlennykh na Chetvertoi mezhdunarodnoi konferentsii po stokhasticheskim metodam”, Teoriya veroyatn. i ee primen., 65:1 (2020), 151–210
•  Number of views: This page: 100 References: 20 First page: 9