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The compact support property for the \(\Lambda\)-Fleming-Viot process with underlying Brownian motion. (English) Zbl 1260.60098
Summary: Using the lookdown construction of Donnelly and Kurtz, we prove that, at any fixed positive time, the \(\Lambda\)-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding \(\Lambda\)-coalescent comes down from infinity not too slowly. We also find both upper bound and lower bound on the Hausdorff dimension for the support.

MSC:
60G57 Random measures
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G17 Sample path properties
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