Gradient estimates of harmonic functions and transition densities for Levy processes

2013/07/26 by Kulczycki, Tadeusz, Ryznar, Michal · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1307.7158

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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• Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

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