Harnack and HWI Inequalities on Infinite-Dimensional Spaces

作     者：Jing Hai SHAO 

作者机构：School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第6期

页      面：1195-1204页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10721091) and the 973-Project (Grant No. 2006CB805901) 

主　　题：Harnack inequality loop groups HWI inequality abstract Wiener space Ornstein- Uhlenbeck semigroup 

摘      要：In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.