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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tvp5245https://doi.org/10.4213/tvp5245 https://www.mathnet.ru/eng/tvp/v64/i3/p456
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Abstract page: | 484 | Full-text PDF : | 82 | References: | 69 | First page: | 22 |
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