Bounded perturbations of two-dimensional diffusion processes with nonlocal conditions near the boundary

TL;DR

This paper investigates conditions under which bounded nonlocal perturbations of elliptic operators generate Feller semigroups for two-dimensional diffusion processes with boundary conditions involving integrals over the domain.

Contribution

It provides new sufficient conditions on nonnegative measures ensuring the perturbed operator generates a Feller semigroup without smallness assumptions.

Findings

Established criteria for nonlocal operators to generate Feller semigroups.

Extended the theory to include non-small boundary measures.

Analyzed bounded perturbations in multidimensional diffusion contexts.

Abstract

We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure of the domain with respect to a nonnegative Borel measure without assuming that the measure is small. We state sufficient conditions on the measure guaranteeing that the corresponding nonlocal operator is the generator of a Feller semigroup.