The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
The stationary Ornstein-Uhlenbeck process on the path space over a compact Riemannian manifold is constructed by finite-dimensional approximation. This solves the corresponding martingale problem. The approximative construction given is more direct than that obtained before by \textit{B. K. Driver} and \textit{M. Röckner} [C. R. Acad. Sci., Paris, Sér. I 315, No. 5, 603-608 (1992; Zbl 0771.58047)], but only gives the process started with the invariant measure (i.e., Wiener measure). It relies on a Kolmogorov-type estimate which uses an explicit formula for the finite-dimensional projections of the Ornstein-Uhlenbeck operator. The Kolmogorov-type estimate is also used to show Hölder continuity of the sample paths of the Ornstein-Uhlenbeck process.
scientific article; zbMATH DE number 987555