Geometric analysis for symmetric Fleming-Viot operators: Rademacher's theorem and exponential families
type: Item
instance of: scholarly article
title: Geometric analysis for symmetric Fleming-Viot operators: Rademacher's theorem and exponential families
zbMATH Open document ID: 1011.60025
DOI: 10.1023/A:1016360318443
author: Alexander Schied
published in: Potential Analysis
publication date: 2002-08-28T00:00:00Z
review text: This paper contains a number of very interesting results about symmetric Fleming-Viot operators and their associated Dirichlet forms. Using the natural geometry of a symmetric Fleming-Viot operator \({\mathcal L}\) the author obtains analytical descriptions of the corresponding Dirichlet space \(({\mathcal E}, {\mathcal D}({\mathcal E}))\). In particular, a complete characterization of functions in \({\mathcal D}({\mathcal E})\) in terms of their differentiability properties along exponential families are given. One of the main results is a Rademacher theorem stating that any function which is Lipschitz continuous with respect to the Bhattacharya distance is contained in \({\mathcal D}({\mathcal E})\) and possesses a bounded gradient. A converse to this statement is also given.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 1790687
zbMATH Keywords: Rademacher's theorem
zbMATH Keywords: Fleming-Viot process
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Bhattacharya distance
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1790687