报告题目：Exit problem as the generalized solution of the Dirichlet problem

报告人： 宋庆硕 教授 香港城市尊龙凯时

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

主办单位：数学学院

报告摘要：We talk aboutsufficient conditionsfor a Feynman-Kac functional up to an exit timeto be the generalized viscosity solution of a Dirichlet problem.The key ingredient is to find out continuity of exit operator underSkorokhod topology, which reveals the intrinsicconnection of overfitting Dirichlet boundary with fine topology.As an application, we establish the sub and supersolutions fora 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 withcomparison principle and Perron's method.