# 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} }

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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