Gradient estimates of harmonic functions and transition densities for Levy processes
Probability
2013-07-30 v1
Abstract
We prove gradient estimates for harmonic functions with respect to a -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 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.
Cite
@article{arxiv.1307.7158,
title = {Gradient estimates of harmonic functions and transition densities for Levy processes},
author = {Tadeusz Kulczycki and Michal Ryznar},
journal= {arXiv preprint arXiv:1307.7158},
year = {2013}
}