报告题目：
Exit problem as the generalized solution of the Dirichlet problem
报告人： 宋庆硕 教授 香港城市大学
报告时间：2018年8月31日下午1:30-2:30
报告地点：数学楼第一报告厅
报告摘要：We talk about
sufficient conditions
for a Feynman-Kac functional up to an exit time
to be the generalized viscosity solution of a Dirichlet problem.
The key ingredient is to find out continuity of exit operator under
Skorokhod topology, which reveals the intrinsic
connection of overfitting Dirichlet boundary with fine topology.
As an application, we establish the sub and supersolutions for
a class of non-stationary HJB (Hamilton-Jacobi-Bellman) equations with fractional Laplacian operator via Feynman-Kac functionals associated to $\alpha$-stable processes, which enables us to verify its solvability together with
comparison principle and Perron's method.
