738 research outputs found

    The compact support property for the Λ\Lambda-Fleming-Viot process with underlying Brownian motion

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    Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the Λ\Lambda-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding Λ\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.Comment: 21 page

    Exact modulus of continuities for Λ\Lambda-Fleming-Viot processes with Brownian spatial motion

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    For a class of Λ\Lambda-Fleming-Viot processes with Brownian spatial motion in Rd\mathbb{R}^d whose associated Λ\Lambda-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 Λ\Lambda-Fleming-Viot support processes. In particular, if the Λ\Lambda-coalescent is the Beta(2β,β)(2-\beta,\beta) coalescent for β(1,2]\beta\in(1,2] with β=2\beta=2 corresponding to Kingman's coalescent, then for h(t)=tlog(1/t)h(t)=\sqrt{t\log (1/t)}, the global modulus of continuity holds for the support process with modulus function 2β/(β1)h(t)\sqrt{2\beta/(\beta-1)}h(t), and both the left and right local modulus of continuity hold for the support process with modulus function 2/(β1)h(t)\sqrt{2/(\beta-1)}h(t).Comment: 28 page
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