2022/06/17 by Liu, Huili, Zhou, Xiaowen · 1 citation
#2020 subject classifications: Primary 60J68 #60G17 #60J95 #FOS: Mathematics #Probability (math.PR) #secondary 60G57
paper · doi:10.48550/arxiv.2206.08840
For a class of Λ-Fleming-Viot processes with Brownian spatial motion in ℝd whose associated Λ-coalescents come down from infinity, we obtain sharp global and local modulus of continuities for the ancestry processes recovered from the lookdown representations. As applications, we prove both global and local modulus of continuities for the Λ-Fleming-Viot support processes. In particular, if the Λ-coalescent is the Beta(2-β,β) coalescent for β∈(1,2] with β=2 corresponding to Kingman's coalescent, then for h(t)=√(tlog (1/t)), the global modulus of continuity holds for the support process with modulus function √(2β/(β-1))h(t), and both the left and right local modulus of continuities hold for the support process with modulus function √(2/(β-1))h(t).