Convergence to Fleming-Viot processes in the weak atomic topology
type: Item
instance of: scholarly article
title: Convergence to Fleming-Viot processes in the weak atomic topology
zbMATH Open document ID: 0817.60029
DOI: 10.1016/0304-4149(94)00006-9
author: Thomas G. Kurtz
author: Stewart N. Ethier
published in: Stochastic Processes and their Applications
publication date: 1995-07-17T00:00:00Z
review text: On the space of finite positive Borel measures on a complete separable metric space, a metric is defined which gives rise to what is called the weak atomic topology. This topology is designed so that convergence is equivalent to the combination of the usual weak convergence plus the convergence in size and location of the atoms of the sequence of measures to those of the limit. In measure-valued diffusion processes used as models for gene frequencies [see for instance \textit{W. H. Fleming} and \textit{M. Viot}, Indiana Univ. Math. J. 28, 817-843 (1979; Zbl 0444.60064)] it may be useful to establish convergence to the limit process or continuity of sample paths in this stronger sense in order to ensure that atoms are behaving in the expected manner. The paper derives conditions under which this can be done and applies them to examples of processes which have previously only been studied under the weaker topology.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 713914
zbMATH Keywords: Fleming-Viot process
zbMATH Keywords: measure-valued diffusion
zbMATH Keywords: convergence in distribution
zbMATH Keywords: weak topology
reviewed by: D. R. Grey
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)00006-9
OpenAlex ID: W2065053277
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description: scientific article; zbMATH DE number 713914