Green's function and invariant density for an integro-differential operator of second order

Abstract

We construct the Green function for a parabolic- elliptic integro- differential operator of second order with boundary conditions given by a first order operator, both with Holder continuous coefficients. Also, we prove the existence of a unique invariant density associated with the corresponding reflected diffusion process with jumps. This allows us to study the asymptotic behaviour of the solution for some oblique derivative problems.