Gradient estimates of harmonic functions and transition densities for Levy processes

Tadeusz Kulczycki; Michal Ryznar

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arXiv · 1307.7158

Gradient estimates of harmonic functions and transition densities for Levy processes

Tadeusz Kulczycki·Michal Ryznar

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Abstract

We prove gradient estimates for harmonic functions with respect to a $d$-dimensional unimodal pure-jump Levy process under some mild assumptions on the density of its Levy measure. These assumptions allow for a construction of an unimodal Levy process in $\R^{d+2}$ with the same characteristic exponent as the original process. The relationship between the two processes provides a fruitful source of gradient estimates of transition densities. We also construct another process called a difference process which is very useful in the analysis of differential properties of harmonic functions.

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BibTeX RIS

Tadeusz Kulczycki, Michal Ryznar. 2013-07-26. Gradient estimates of harmonic functions and transition densities for Levy processes. https://arxiv.org/abs/1307.7158

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