Finite dimensional approximation of Riemannian path space geometry.
type: Item
instance of: scholarly article
title: Finite dimensional approximation of Riemannian path space geometry.
zbMATH Open document ID: 1041.58013
DOI: 10.1016/S0022-1236(02)00095-2
author: Ana Bela Cruzeiro
author: Xicheng Zhang
published in: Journal of Functional Analysis
publication date: 2004-02-03T00:00:00Z
review text: The paper deals with the geometry of path space over a compact Riemannian manifold. The Riemannian geometry of this space in known to have many complicated features and difficulties, partly overcome previously by introducing the called Markovian connection (Riemannian with non-zero torsion). Here the authors construct a finite-dimensional approximation for path space based on finite partitions of the time interval that allows one to determine the horizontal lift of the Ornstein-Uhlenbeck processes through the Markovian connection as well as to prove a representation formula for the heat semigroup on adapted vector fields and a communication formula for its derivative.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 58D15
zbMATH DE Number: 2037129
zbMATH Keywords: finite dimensional approximations
zbMATH Keywords: Markovian connection
zbMATH Keywords: integration by parts
zbMATH Keywords: interwinning formula
zbMATH Keywords: heat semigroup
zbMATH Keywords: horizontal lift
zbMATH Keywords: Ornstein-Uhlenbeck process
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
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full work available at URL: s0022-1236(02)00095-2
OpenAlex ID: W2022179512
description: scientific article; zbMATH DE number 2037129