Decay rate of harmonic functions for non-symmetric strictly $\alpha$-stable L\'evy processes

Abstract

In this paper we investigate functions that are harmonic with respect to the non-symmetric strictly $\alpha$-stable L\'evy processes on an open set $D \in \mathbb{R}^d$. We obtain the explicit formula for their boundary decay rate at parts of the boudary of $D$ outside of which they vanish.