报告题目：Refracted Oscillating Brownian Motion
报告时间：2025-11-12 10:00-11:00
报 告 人 ：周晓文 教授（加拿大康卡迪亚大学）
报告地点：雷军科技楼六楼报告厅（644）
Abstract:
Motivated by problems in stochastic control, we consider the unique solution X to the following SDE
dX_t=(μ_11_{X_t≤0}+μ_21_{X_t>0})d_t+(σ_11_{X_t≤0}+σ_21_{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.
To find the transition density, 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 density is obtained by inverting the Laplace transform.
We will also present more recent work on threshold diffusion.
This talk is based on joint work with Zengjing Chen, Panyu Wu and Weihai Zhang, and with Lina Ji and Chuyang Li.
