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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


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.


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J. R. Norris. "Ornstein-Uhlenbeck processes indexed by the circle." Ann. Probab. 26 (2) 465 - 478, April 1998.


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

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

Primary: 58G32 , 60G15 , 60J60

Keywords: Brownian motin of loops , Gaussian processes , Ornstein-Uhlenbeck process , two-sided Markov property

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 2 • April 1998
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