报 告 人：周晓文，加拿大Concordia 大学数学与统计系终身教授

报告时间：2026年7月13日星期一下午3:40-4:40，览秀楼105

#腾讯会议：362-683-9628

报告摘要：Motivated by problems in stochastic control, we consider the unique solution X to the following SDE dX_t = (μ_1 1{X_t≤0} + μ_2 1{X_t>0})dt + (σ_1 1{X_t≤0} + σ_2 1{X_t>0})dB_t for μ_1, μ_2 ∈ R and σ_1, σ_2 > 0.

For μ_1 = μ_2 an explicit expression for transition density of X was obtained by Keilson and Wellner (1978). For σ_1 = σ_2 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.

报告人简介：周晓文教授，于1988年及1991年在中山大学分别获得本科和硕士学位，于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,随机微分方程及其在种群遗传学和风险理论中的应用。先后在AP,PTRF, AAP, AIHP,Bernoulli, SPA, JDE,SICON, IEEE TAC，IME 等国际期刊发表论文90余篇。