The logarithmic Sobolev inequality for the Wasserstein diffusion

• 成果类型: Article
• 署名作者: Doering, Maik; Stannat, Wilhelm
• 署名单位: Technical University of Darmstadt
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0166-6
• 发表日期: 2009
• 页码: 189-209
• 关键词: semigroups

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.