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}
}
  • P. KimR. Song
  • 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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