The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
type: Item
instance of: scholarly article
title: The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
zbMATH Open document ID: 0888.58074
author: Tetsuya Kazumi
published in: Journal of Functional Analysis
publication date: 1998-06-08T00:00:00Z
review text: The stationary Ornstein-Uhlenbeck process on the path space over a compact Riemannian manifold is constructed by finite-dimensional approximation. This solves the corresponding martingale problem. The approximative construction given is more direct than that obtained before by \textit{B. K. Driver} and \textit{M. Röckner} [C. R. Acad. Sci., Paris, Sér. I 315, No. 5, 603-608 (1992; Zbl 0771.58047)], but only gives the process started with the invariant measure (i.e., Wiener measure). It relies on a Kolmogorov-type estimate which uses an explicit formula for the finite-dimensional projections of the Ornstein-Uhlenbeck operator. The Kolmogorov-type estimate is also used to show Hölder continuity of the sample paths of the Ornstein-Uhlenbeck process.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 58B99
zbMATH DE Number: 987555
zbMATH Keywords: martingale problem
zbMATH Keywords: path space
zbMATH Keywords: Ornstein-Uhlenbeck process
zbMATH Keywords: Hölder continuity
zbMATH Keywords: finite dimensional approximation
MaRDI profile type: Publication
full work available at URL: jfan.1996.2988
OpenAlex ID: W1993717503
DOI: 10.1006/JFAN.1996.2988
description: scientific article; zbMATH DE number 987555