The logarithmic Sobolev inequality for the Wasserstein diffusion

被引：12

作者：

Doering, Maik ^{[1
]}

Stannat, Wilhelm ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 145卷 / 1-2期

关键词：

SEMIGROUPS;

D O I：

10.1007/s00440-008-0166-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev inequality. This implies hypercontractivity of the associated transition semigroup. We also study functional inequalities for related diffusion processes.

引用

页码：189 / 209

页数：21

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