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Ergodicity of finite-energy diffusions


Author: Timothy C. Wallstrom
Journal: Trans. Amer. Math. Soc. 318 (1990), 735-747
MSC: Primary 81C20; Secondary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1990-0986032-1
MathSciNet review: 986032
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0986032-1
Keywords: Ergodic theory, finite-energy diffusions, singular diffusions, coefficient of ergodicity, spin, stochastic mechanics
Article copyright: © Copyright 1990 American Mathematical Society

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