Speaker: Dr. Jesus Contreras ，CIMAT

Inviter: 石权副研究员

Title: On local times of spectrally one-sided Lévy processes

Language: Chinese

Time & Venue: 2024.11.06 10:30-11:30 南楼N620

Abstract: Given a Lévy process, the study of its local times up to a stopping time T as a process in the space variable has been a matter of research interest since the decade of 1960, with the initial works of F. Knight and J. Ray for the Brownian motion. They established the so-called Ray-Knight theorems, describing the joint distribution of local times in terms of squared Bessel processes when T is a first passage time or the inverse of the local time at 0. In this talk, we present some analogue results for the local times of spectrally one-sided Lévy processes, which differ depending on its path behavior. In the unbounded variation case, an excursion theory approach will be used, whilst for the bounded variation case we will explore a connection with a population model, trees and the Crump-Mode-Jagers (CMJ) process.