Ergodicity of Finite-Energy Diffusions
Timothy C. Wallstrom · Transactions of the American Mathematical Society · 1990
Recently, the existence of a class of diffusion processes with highly singular drift coefficients has been established under the assumption of "finite energy." The drift singularities of these diffusions greatly complicate their ergodicity properties; indeed, they can render the diffusion nonergodic. In this paper, a method is given for estimating the relaxation time of a finite-energy diffusion, when it is ergodic. These results are applied to show that the set of $\operatorname {spin} - \tfrac {1} {2}$ diffusions of stochastic mechanics is uniformly ergodic.