Some support properties of $ Lambda$-Fleming-Viot process with Brownian mutation
主 题: Some support properties of $ Lambda$-Fleming-Viot process with Brownian mutation
报告人: Prof. Xiaowen Zhou (Concordia University, Canada)
时 间: 2012-07-13 9:00-10:00
地 点: 理科一号楼 1418
The $\\Lambda$-Fleming-Viot process generalizes the classical Fleming-Viot process in population genetics. It is a probability-measure-valued process whose dual process involves the $\\Lambda$-coalescent, the coalescent with multiple collisions. For such a process with Brownian spatial motion, it was shown by Blath that it does not allow a compact support as long as the corresponding $\\Lambda$-coalescent stays infinite. Applying the lookdown construction we can show that the process has a compact support at any fixed positive time given that the $\\Lambda$-coalescent does not come down from infinity too slowly. We also find an upper bound on the Hausdorff dimension for the support. These results generalize the early results of Dawson and Hochberg on the classical
