English

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}
}

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16 pages