Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump
Probability
2009-08-21 v1 Functional Analysis
Abstract
The Harnack inequality established in [13] for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed equivalent, and thus sharp, for the Gaussian case. As an application of the log-Harnack inequality, the HWI inequality is established for the Gaussian case. Perturbations with linear growth are also investigated.
Keywords
Cite
@article{arxiv.0908.2889,
title = {Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump},
author = {Shun-Xiang Ouyang and Michael Röckner and Feng-Yu Wang},
journal= {arXiv preprint arXiv:0908.2889},
year = {2009}
}
Comments
16 pages