Convergence to Fleming-Viot processes in the weak atomic topology
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.
scientific article; zbMATH DE number 713914
scientific article