Continuity of $l^2$-Valued Ornstein-Uhlenbeck Processes
Open Access
- 1 January 1990
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 18 (1) , 68-84
- https://doi.org/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 $l^2$.
Keywords
This publication has 0 references indexed in Scilit: