Transportation cost inequalities on path and loop groups
type: Item
instance of: scholarly article
title: Transportation cost inequalities on path and loop groups
zbMATH Open document ID: 1068.60013
author: Shizan Fang
author: Jinghai Shao
published in: Journal of Functional Analysis
publication date: 2005-02-22T00:00:00Z
review text: The transportation cost inequalities compare the square of the Wasserstein distance between a measure \(\mu\) on a metric space \(X\) and the measure \(f\mu\), where \(f\) is a positive continuous function, with the corresponding Kullback information; see \textit{H. Djellout, A. Guillin} and \textit{L. Wu} [Ann. Probab. 32, No. 3B, 2702--2732 (2004; Zbl 1061.60011)] for a brief survey of results in this direction for various classes of spaces and measures. The authors consider the case where \(X\) is the path space on a connected Lie group, and \(\mu\) is the appropriate generalization of the Wiener measure. They introduce and study a distance on \(X\) and prove the corresponding transportation cost inequality. The case, where \(X\) is the path space on the loop group over a Lie group, is also considered.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 2136761
zbMATH Keywords: Wasserstein distance
zbMATH Keywords: Kullback information
zbMATH Keywords: path group
MaRDI profile type: Publication
full work available at URL: j.jfa.2004.02.002
OpenAlex ID: W2034508498
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DOI: 10.1016/J.JFA.2004.02.002
description: scientific article; zbMATH DE number 2136761