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January, 1989 Large Deviations for $l^2$-Valued Ornstein-Uhlenbeck Processes
I. Iscoe, D. McDonald
Ann. Probab. 17(1): 58-73 (January, 1989). DOI: 10.1214/aop/1176991494


A stationary $l^2$-valued Ornstein-Uhlenbeck process given formally by $dX(t) = - AX(t) dt + \sqrt{2a} dB(t)$, where $A$ is a positive self-adjoint constant operator on $l^2$ and $B(t)$ is a cylindrical Brownian motion on $l^2$, is considered. An upper bound on $P(\sup_{t \in \lbrack 0, T \rbrack}\|X(t)\| > x)$ is established and the asymptotics for the given bound, as $x \rightarrow \infty$, is derived.


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I. Iscoe. D. McDonald. "Large Deviations for $l^2$-Valued Ornstein-Uhlenbeck Processes." Ann. Probab. 17 (1) 58 - 73, January, 1989.


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

zbMATH: 0716.60060
MathSciNet: MR972771
Digital Object Identifier: 10.1214/aop/1176991494

Primary: 60H10
Secondary: 60G15 , 60G17

Keywords: Dirichlet form , Hilbert space , large deviations , Ornstein-Uhlenbeck

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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