The derivative martingale in a branching Levy process
数学专题报告
报告题目(Title)：The derivative martingale in a branching Levy process
报告人(Speaker)：石权 （中科院应用数学所）
地点(Place)：后主楼1225
时间(Time)：2022年1月6日 下午4.00-5.00
邀请人(Inviter)：何辉
报告摘要
A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We obtain a necessary and sufficient condition for the convergence of the derivative martingale of such a process to a non-trivial limit in terms of $(\sigma^2,a,\Lambda)$. This extends previously known results on branching Brownian motions and branching random walks. To obtain this result, we rely on the spinal decomposition and establish a novel zero-one law on the perpetual integrals of centred L\'evy processes conditioned to stay positive.This is joint work with Bastien Mallein.
