报告题目：Brownian motion with two-valued drift and variance

报 告 人：周晓文 教授

报告时间：2024年6月19日下午 4点

报告地点：数统院307报告厅

报告摘要：Motivation by problems in stochastic control, we consider the unique solution X to the following SDE

dXt = (µ11{Xt≤0} + µ21{Xt>0})dt + (σ11{Xt≤0} + σ21{Xt>0})dBt

for µ1, µ2 ∈R and σ1, σ2 > 0. For µ1 = µ2 an explicit expression for transition density of X was obtained by Keilson and Wellner (1978). For σ1 = σ2 the transition density was obtained by Karatzas and Shreve (1984). But the transition density for general X was not known. We first solve the exit problem to process X, and then adopt a perturbation approach to find an expression of potential measure for X. The transition density is found by inverting the Laplace transform.

This talk is based on joint work with Zengjing Chen and Panyu Wu.

报告人简介：周晓文教授, 1999年在美国加州大学Berkeley分校获统计学博士学位。现任加拿大Concordia大学数学与统计系终身教授。长期从事概率论与随机过程理论的研究，主要研究兴趣包括测度值随机过程，Levy过程及其在种群遗传学和风险理论中的应用。先后在《 Annals of Probability》《Probability and Related Fields》《Journal of Differential Equations》《Canadian Journal of Mathematics》《Theoretical Population Biology》《Stochastic Processes and their Applications》《Journal of Theoretical Probability》等国际顶级概率刊物发表论文80余篇。