报告题目：Asymptotic behaviors of subcritical branching killed L\'evy process
时 间：2025年5月28日（星期三）15:30
地 点：理工北楼601
主 办：数学与统计学院
参加对象：概率统计系及其他感兴趣的师生
报告摘要：In this work, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed L\'{e}vy process $X$ in $\mathbb{R}$. Let $\zeta$ denote the extinction time, $M_t$ be the maximal position of all the particles alive at time $t$, and $M:=\sup_{t\ge 0}M_t$ be the all-time maximum. Under the assumption that the offspring distribution satisfies the $L\log L$ condition and some conditions on the spatial motion, we find the decay rate of the survival probability $\mathbb{P}_x(\zeta>t)$ and the tail behavior of $M_t$ as $t\to\infty$. As a consequence, we establish a Yaglom-type theorem. Especially, when the spatial motion is a spectrally negative L\'{e}vy process, we also find the asymptotic behavior of $\mathbb{P}_x(M>y)$ as $y\to\infty$.
报告人简介： 朱雅萍，北京大学博雅博士后，博士毕业于北京师范大学。主要研究内容为分枝布朗运动、分枝莱维过程，已在《Electron. J. Probab.》、《Adv. in Appl. Probab.》等国际期刊发表数篇论文。