This article is cited 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.

MSC: 60J35 60J80 60B99

Received: 21.08.2018
Revised: 27.12.2018
Accepted: 24.01.2019

DOI: 10.4213/tvp5245

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

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