A functional ergodic theorem for the occupation time process of a branching system
type: Item
instance of: scholarly article
title: A functional ergodic theorem for the occupation time process of a branching system
zbMATH Open document ID: 1146.60071
author: Anna Talarczyk
published in: Statistics \& Probability Letters
publication date: 2008-06-05T00:00:00Z
review text: The author considers a system of particles in \(\mathbb{R}^d\) which starts from a Poisson random measure with the intensity being the Lebesgue measure. The particles move independently according to a spherically symmetric \(\alpha\)-stable Lévy motion. They undergo critical branching and the pgf of the branching mechanism is \(G(s)=s+(1+\beta)^{-1}(1-s)^{1+\beta}\) for some \(\beta\in (0,1]\). It is proved that in the critical dimension \(d=\alpha/\beta\) the rescaled occupation time process of the just described \((d,\alpha,\beta)\)-branching particle system converges in law on \(C([0,1], S^\prime(\mathbb{R}^d))\) to a non-trivial non-negative infinitely divisible process with explicitly given Laplace-Stieltjes transform.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 5285352
zbMATH Keywords: \((d,\alpha, \beta)\)-branching particle system
zbMATH Keywords: functional limit theorem
zbMATH Keywords: infinitely divisible process
reviewed by: Alexander Iksanov
MaRDI profile type: Publication
full work available at URL: j.spl.2007.09.010
OpenAlex ID: W2056129418
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DOI: 10.1016/J.SPL.2007.09.010
description: scientific article; zbMATH DE number 5285352