758 research outputs found
The compact support property for the -Fleming-Viot process with underlying Brownian motion
Using the lookdown construction of Donnelly and Kurtz we prove that, at any
fixed positive time, the -Fleming-Viot process with underlying
Brownian motion has a compact support provided that the corresponding
-coalescent comes down from infinity not too slowly. We also find both
upper bound and lower bound on the Hausdorff dimension for the support.Comment: 21 page
Exact modulus of continuities for -Fleming-Viot processes with Brownian spatial motion
For a class of -Fleming-Viot processes with Brownian spatial motion
in whose associated -coalescents come down from
infinity, we obtain sharp global and local modulus of continuities for the
ancestry processes recovered from the lookdown constructions. As applications,
we prove both global and local modulus of continuities for the
-Fleming-Viot support processes. In particular, if the
-coalescent is the Beta coalescent for
with corresponding to Kingman's coalescent, then for
, the global modulus of continuity holds for the
support process with modulus function , and both
the left and right local modulus of continuity hold for the support process
with modulus function .Comment: 28 page
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