论文标题
$λ$ -Fleming-Viot流程的确切连续性模量与布朗空间运动
Exact modulus of continuities for $Λ$-Fleming-Viot processes with Brownian spatial motion
论文作者
论文摘要
对于一类$λ$ -Fleming-Viot流程，带有$ \ Mathbb {r}^d $中的布朗空间运动的过程，其相关的$λ$ -CoaleScents来自Infinity，我们从Bookdown表示恢复的祖先过程中获得了敏锐的全球和地方模量。作为应用程序，我们证明了$λ$ -Fleming-Viot支持流程的全球和本地模量。特别是，如果$λ$ -Coalescent是beta $（2-β，β）$ colescent，$β\ in（1,2] $，$β= 2 $对应于Kingman的合并，则以$ h（t）= \ sqrt {t）= \ sqrt {t \ log（1/t）$，全球模量的连续disulus of Suptuls of Suptul of Suptuls of Contunlus of Contuctus of Contulus of Moduls of Moduls of Moduls of Moduls of Suptuls of Suptuls of Modus of Suptuls of Nods $ \ sqrt {2β/（β-1）} h（t）$，并且使用模量函数$ \ sqrt {2/（β-1）} h（t）$的左右局部局部模量连续性均具有支持过程。
For a class of $Λ$-Fleming-Viot processes with Brownian spatial motion in $\mathbb{R}^d$ 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 $β\in(1,2]$ with $β=2$ corresponding to Kingman's coalescent, then for $h(t)=\sqrt{t\log (1/t)}$, the global modulus of continuity holds for the support process with modulus function $\sqrt{2β/(β-1)}h(t)$, and both the left and right local modulus of continuities hold for the support process with modulus function $\sqrt{2/(β-1)}h(t)$.
