| In this thesis we study the problem of reversibility for certain classes of diffusion processes in finite and infinite dimensions. In the finite dimensional case we look at the generator of Brownian motion with drift, and we present two characterizations of reversibility: the criterion of Kolmogorov which establishes that reversibility is possible if and only if the drift is of gradient form, and a criterion proving that reversibility of a measure is equivalent to quasi-invariance under the group of all translations with a cocycle given in terms of the drift coefficients. Later we use the ideas from the second characterization in finite dimensions to explore the property of reversibility for an Ornstein-Uhlenbeck process with values in an infinite dimensional Hilbert space. |
