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数学学院、所系列学术报告(824场):宋庆硕教授 香港城市大学

发表于: 2018-08-27 14:50  点击:
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.