Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces

Abstract

In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes on metric measure spaces. We show that if $\infty$ is accessible from an open set $D$, then there is only one Martin boundary point of $D$ associated with it, and this point is minimal. We also prove the analogous result for finite boundary points. As a consequence, we show that minimal thinness of a set is a local property.

Definition of the infinite Martin boundary point modified; Corollary 1.4 added; 54 pages