首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Wasserstein space over the Wiener space
Authors:Shizan Fang  Jinghai Shao  Karl-Theodor Sturm
Institution:1. I.M.B, Université de Bourgogne, BP 47870, 21078, Dijon, France
2. School of Mathematics, Beijing Normal University, 100875, Beijing, China
3. Institut für Angewandte Mathematik, Universit?t Bonn, 53115, Bonn, Germany
Abstract:The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves with solutions of the Ornstein–Uhlenbeck evolution equation.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号