Chapman-Enskog-Hilbert expansion for the Ornstein-Uhlenbeck process and the approximation of Brownian motion
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- by Richard S. Ellis PDF
- Trans. Amer. Math. Soc. 199 (1974), 65-74 Request permission
Abstract:
Let $(x(t),\upsilon (t))$ denote the joint Ornstein-Uhlenbeck position-velocity process. Special solutions of the backward equation of this process are studied by a technique used in statistical mechanics. This leads to a new proof of the fact that, as $\varepsilon \downarrow 0,\varepsilon x(t/{\varepsilon ^2})$ tends weakly to Brownian motion. The same problem is then considered for $\upsilon (t)$ belonging to a large class of diffusion processes.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 199 (1974), 65-74
- MSC: Primary 60J60
- DOI: https://doi.org/10.1090/S0002-9947-1974-0353469-4
- MathSciNet review: 0353469