Translator Disclaimer
April 1998 Ornstein-Uhlenbeck processes indexed by the circle
J. R. Norris
Ann. Probab. 26(2): 465-478 (April 1998). DOI: 10.1214/aop/1022855640

Abstract

We consider the class of stationary, zero-mean Gaussian processes, indexed by the circle, satisfying a two-point Markov property and taking values in a vector bundle over the circle with given holonomy. We establish, subject to certain additional symmetry properties, a classification of all such processes. We then propose a construction of a Brownian motion of loops, in which these processes provide the infinitesimal increments.

Citation

Download Citation

J. R. Norris. "Ornstein-Uhlenbeck processes indexed by the circle." Ann. Probab. 26 (2) 465 - 478, April 1998. https://doi.org/10.1214/aop/1022855640

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0940.60052
MathSciNet: MR1626166
Digital Object Identifier: 10.1214/aop/1022855640

Subjects:
Primary: 58G32, 60G15, 60J60

Rights: Copyright © 1998 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.26 • No. 2 • April 1998
Back to Top