Finite dimensional approximation of Riemannian path space geometry

Ana Bela Cruzeiro; Xicheng Zhang

doi:10.1016/S0022-1236(02)00095-2

Finite dimensional approximation of Riemannian path space geometry

Ana Bela Cruzeiro^*, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative.

Original language	English
Pages (from-to)	206-270
Number of pages	65
Journal	Journal of Functional Analysis
Volume	205
Issue number	1
DOIs	https://doi.org/10.1016/S0022-1236(02)00095-2
Publication status	Published - 1 Dec 2003
Externally published	Yes

Keywords

Finite dimensional approximation
Heat semigroup
Horizontal lift of OU process
Integration by parts
Intertwinning formula
Markovian connection

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10.1016/S0022-1236(02)00095-2

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abstract = "In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative.",

keywords = "Finite dimensional approximation, Heat semigroup, Horizontal lift of OU process, Integration by parts, Intertwinning formula, Markovian connection",

author = "Cruzeiro, {Ana Bela} and Xicheng Zhang",

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AU - Zhang, Xicheng

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AB - In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative.

KW - Finite dimensional approximation

KW - Heat semigroup

KW - Horizontal lift of OU process

KW - Integration by parts

KW - Intertwinning formula

KW - Markovian connection

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VL - 205

SP - 206

EP - 270

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

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Finite dimensional approximation of Riemannian path space geometry

Abstract

Keywords

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