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

TL;DR

This paper derives explicit formulas for how harmonic functions related to non-symmetric strictly alpha-stable Levy processes decay near the boundary of a domain, enhancing understanding of their boundary behavior.

Contribution

It provides the first explicit boundary decay rate formulas for harmonic functions associated with non-symmetric strictly alpha-stable Levy processes.

Findings

Explicit boundary decay rate formulas derived

Boundary behavior characterized outside the domain

Enhanced understanding of non-symmetric Levy process harmonic functions

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.