| We apply the methods of probabilistic potential theory and Dirichlet forms to the study of a class of infinite dimensional stochastic processes, which includes the Ornstein-Uhlenbeck process. We obtain criteria for the sample path continuity of the process in a suitable Hilbert space, in terms of its invariant measure and diffusion coefficients. Applied to Ornstein-Uhlenbeck process these yield extensions of results given previously by other authors. By looking at the properties of its Dirichlet form, we deduce that the Ornstein-Uhlenbeck process is 'quasi-ergodic' in general, and genuinely ergodic when the drift is not too small. As well, we consider some local properties of the process such as the regularity of boundary points and the law of the iterated logarithm.;To conclude we present some open questions concerning these infinite dimensional Ornstein-Uhlenbeck processes. |
