Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump

Details Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump

2009-08-20

arxiv.org/abs/0908.2889v1

Mathematics

Probability

16 pages

Scientific paper

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.

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