Probability and Statistics Seminar——Exceptional times for the instantaneous propagation of superprocess
报告人：Jieliang Hong (Technion)
时间：2022-11-07 15:00-16:00
地点：Room 1114, Sciences Building No. 1
Abstract:
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of $X_t$ is the whole space for almost all $t>0$ before extinction, the so-called ``instantaneous propagation'' property. We prove that exceptional times exist at which the support is compact and nonempty. Moreover, the set of exceptional times is dense and its Hausdorff dimension equals $1$. This talk is based on a joint work with Leonid Mytnik.
About the Speaker:
Jieliang Hong is a postdoc at Technion-Israel Institute of Technology. He obtained his Bachelor's degree from Peking University in 2015. Later in 2021 he obtained the Ph.D degree at the University of British Columbia under the supervision of Prof. Edwin Perkins. His research interests include superprocess, SPDE, branching process, and interacting particle system.
