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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ergodicity of finite-energy diffusions

Author: Timothy C. Wallstrom
Journal: Trans. Amer. Math. Soc. 318 (1990), 735-747
MSC: Primary 81C20; Secondary 60J60
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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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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