Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

Chapman-Enskog-Hilbert expansion for the Ornstein-Uhlenbeck process and the approximation of Brownian motion


Author: Richard S. Ellis
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60J60

Retrieve articles in all journals with MSC: 60J60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0353469-4
Keywords: Chapman-Enskog-Hilbert expansion, Ornstein-Uhlenbeck process, Brownian motion, essentially selfadjoint operator, weak solution of a partial differential equation, diffusion process
Article copyright: © Copyright 1974 American Mathematical Society