Stopped Markov Processes and Applications to the Dirichlet Problem in a Smooth Domain
2009, v.15, №4, 549-562
In this paper, we generalize a theorem due to Dynkin about stopped Markov processes and use this result to generalize a well-known theorem from the theory of diffusion processes. We then use this latter theorem to show that certain probabilistic functionals of a time-homogeneous diffusion process are solutions of the corresponding Dirichlet problem in a smooth bounded domain in Euclidean space.
Keywords: stopped Markov processes,Dirichlet problem