Solvability of General Solution and a Related Exit Problem

Dr. Qingshuo Song
Worcester Polytechnic Institute
Associate Professor

“We study 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 the continuity of exit operator under the Skorokhod topology, which reveals the intrinsic connection between overfitting Dirichlet boundary and 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 lead to the existence of strong solution to the original HJB equation. It’s a joint work with Yuecai Han and Gu Wang.”

Light refreshments will be served @ 3:00pm in EMS E424A.