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July, 1989 The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process
J. C. Taylor
Ann. Probab. 17(3): 1055-1062 (July, 1989). DOI: 10.1214/aop/1176991256


A process $(X_t)$ is equivalent to an Ornstein-Uhlenbeck process if and only if $e^{-\lambda t}f(X_t)$ is a martingale for every $f \geq 0$ on $\mathbb{R}^d$ such that $\Delta f(x) - \langle x, \nabla f(x)\rangle = \lambda f(x)$.


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J. C. Taylor. "The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process." Ann. Probab. 17 (3) 1055 - 1062, July, 1989.


Published: July, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0686.60084
MathSciNet: MR1009444
Digital Object Identifier: 10.1214/aop/1176991256

Primary: 60J60
Secondary: 60G44

Keywords: characterization , Eigenfunctions , Martingales , Ornstein-Uhlenbeck process

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 3 • July, 1989
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