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[In this article, we discuss two of the main prototypes of measure-valued processes, namely the classical Fleming-Viot and Dawson-Watanabe processes, and some of their recent generalizations. In particular, we show how the so-called lookdown construction of Donnelly and Kurtz can be used to reveal interesting structural and path-properties of the (generalized) processes in the case when the underlying motion and branching mechanisms satisfy certain self-similarity properties. As applications of the method, we first discuss the notion of a ‘flickering random measure’, and then conclude with remarks about properties of the support of general, and in particular Beta-, Fleming-Viot processes.]
Published: Dec 30, 2009
Keywords: Primary: 60G57; Secondary: 60G17; Generalized Fleming-Viot process; flickering random measures; super-Brownian motion; Dawson-Watanabe process; measure-valued diffusion; coalescent; lookdown construction; wandering random measure; Neveu superprocess
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