Ergodicity of finite-energy diffusions

Wallstrom, Timothy C.

doi:10.1090/S0002-9947-1990-0986032-1

Ergodicity of finite-energy diffusions
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Trans. Amer. Math. Soc. 318 (1990), 735-747 Request permission

Abstract:

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.

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