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January, 1990 Continuity of $l^2$-Valued Ornstein-Uhlenbeck Processes
I. Iscoe, M. B. Marcus, D. McDonald, M. Talagrand, J. Zinn
Ann. Probab. 18(1): 68-84 (January, 1990). DOI: 10.1214/aop/1176990938

Abstract

A stationary $l^2$-valued Ornstein-Uhlenbeck process is considered which is given formally by $dX_t = -AX_t dt + \sqrt 2a dB_t$, where $A$ is a positive self-adjoint operator on $l^2, B_t$ is a cylindrical Brownian motion on $l^2$ and $a$ is a positive diagonal operator on $l^2$. A simple criterion is given for the almost-sure continuity of $X_t$ in $l^2$ which is shown to be quite sharp. Furthermore, in certain special cases, we obtain simple necessary and sufficient conditions for the almost-sure continuity of $X_t$ in $l^2$.

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I. Iscoe. M. B. Marcus. D. McDonald. M. Talagrand. J. Zinn. "Continuity of $l^2$-Valued Ornstein-Uhlenbeck Processes." Ann. Probab. 18 (1) 68 - 84, January, 1990. https://doi.org/10.1214/aop/1176990938

Information

Published: January, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0699.60052
MathSciNet: MR1043937
Digital Object Identifier: 10.1214/aop/1176990938

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

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 1 • January, 1990
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