Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 60H10
Secondary: 60G15, 60G17

Rights: Copyright © 1989 Institute of Mathematical Statistics

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.17 • No. 1 • January, 1989
Back to Top