# Potential theory of truncated stable processes

@article{Kim2006PotentialTO,
title={Potential theory of truncated stable processes},
author={Panki Kim and Renming Song},
journal={Mathematische Zeitschrift},
year={2006},
volume={256},
pages={139-173}
}
• Published 18 May 2006
• Mathematics
• Mathematische Zeitschrift
For any $$\alpha \in (0, 2)$$, a truncated symmetric α-stable process is a symmetric Lévy process in $$\mathbb{R}^{d}$$ with a Lévy density given by $$c|x|^{-d-\alpha} 1_{\{|x| < 1\}}$$ for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to…
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