We consider the generalized Dirichlet problem associated to Integro-Differential operator. Different from the analytical approach, a probabilistic approach is established by observing the sufficient condition on continuity of stopping time with respect to Skorohod topology. Some examples will be provided to compare with the results from the analytical approach from the existing literatures.

Dr. Qingshuo Song is currently working at Department of Mathematics of City University of Hong Kong as an associate professor. His research interests include stochastic control theory, and its applications in mathematical finance and engineering. Dr. Qingshuo Song received his BSc and MA from Nankai University in 1996 and 1999, MA and PhD from Department of Mathematics of Wayne State University in 2003 and 2006. Prior to joining City University of Hong Kong in 2010, Dr. Qingshuo Song had been working with Department of Mathematics of University of Michigan in 2009 and Department of Mathematics of University of Southern California during 2006-2009.