Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes

Tomasz Grzywny and Mateusz Kwaśnicki

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 1-38

Abstract: In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unimodal Lévy processes. We also prove a supremum estimate and a regularity result for functions harmonic with respect to a general isotropic unimodal Lévy process.

Keywords: Potential theory; Lévy process; Isotropic unimodal distribution; Hitting time; Harnack inequality (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:1:p:1-38

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DOI: 10.1016/j.spa.2017.04.004

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