学术讲座

报告题目：Refracted ocsilating Brownian motion

报告时间：2025年06月06日（周五）上午10:00-10:30

报告专家：加拿大Concordia大学周晓文教授

报告地点：湘江楼A926

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

dX_t = (µ₁1{X_t≤0} + µ₂1{X_t>0})dt + (σ₁1{X_t≤0} + σ₂1{X_t>0})dB_t

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, Panyu Wu and Weihai Zhang.

专家简介：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 Theory and Related Fields、Annals of Applied Probability、Annales De L Institut Henri Poincare、Journal of Differential Equations、Stochastic Processes and their Applications、Journal of Theoretical Probability、Insurance, Mathematics & Economics、Theoretical Population Biology等国际期刊发表论文90余篇。