Martin boundary for some symmetric Lévy processes

Abstract

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric Lévy processes in ${\mathbb R}^d$. We show that, if $D\subset {\mathbb R}^d$ is an open set which is $κ$-fat at a boundary point $Q\in \partial D$, then there is exactly one Martin boundary point associated with $Q$ and this Martin boundary point is minimal.