On Martingale Problems and Feller Processes

Original · EN

Let A be a pseudo-differential operator with negative definite symbol q. In this paper we establish a sufficient condition such that the well-posedness of the (A,Cc∞(Rᵈ))-martingale problem implies that the unique solution to the martingale problem is a Feller process. This provides a proof of a former claim by van Casteren. As an application we prove new existence and uniqueness results for Lévy-driven stochastic differential equations and stable-like processes with unbounded coefficients.