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

Summary 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 Hölder 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.This research have been supported in part by Ministero P.I. « Progetto Caleolo delle Variazioni » and N.S.F. under grant No. DMS-8702236.