Harnack Inequalities and Applications for Ornstein–Uhlenbeck Semigroups with Jump

被引：0
作者：
Shun-Xiang Ouyang
Michael Röckner
Feng-Yu Wang
机构：
[1] Bielefeld University,Department of Mathematics
[2] Beijing Normal University,School of Mathematical Sciences
[3] Swansea University,Department of Mathematics
来源：
Potential Analysis | 2012年 / 36卷
关键词：
Harnack inequality; Ornstein–Uhlenbeck process; Lévy process; Entropy-cost inequality; 60J75; 47D07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The Harnack inequality established in Röckner and Wang (J Funct Anal 203:237–261, 2003) 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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页码：301 / 315
页数：14
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