The moment analysis of a branching random walk on a lattice with a single source
type: Item
instance of: scholarly article
title: The moment analysis of a branching random walk on a lattice with a single source
zbMATH Open document ID: 0963.60083
author: E. B. Yarovaya
author: Leonid V. Bogachev
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The paper investigates the asymptotic behavior of the continuous-time branching random walk on \(Z^d, d\geq 1\), in which particles may produce children only at a fixed point (source) of the lattice. Assuming that the random walk is homogeneous, irreducible and with jumps having zero mean and finite varince, the authors investigate the limiting behavior of the integer moments of the total number of particles in the process and the integer moments of the number of particles at fixed points of the lattice. They show, in particular, that for the critical processes the asymptotic representations of the mentioned moments are essentially different for \(d=1,2,3,4\) and \(d\geq 5\).
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1557544
zbMATH Keywords: Bellman-Harris branching process
zbMATH Keywords: source
zbMATH Keywords: random walk
zbMATH Keywords: moments
reviewed by: Vladimir Vatutin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557544