On the Convergence of Karhunen-Loeve Series Expansion for a Brownian Particle

[+] Author and Article Information
W. G. Paff, G. Ahmadi

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699

J. Appl. Mech 60(3), 783-784 (Sep 01, 1993) (2 pages) doi:10.1115/1.2900876 History: Received December 10, 1990; Revised August 17, 1992; Online March 31, 2008


A linear Langevin equation for the velocity of a Brownian particle is considered. The equation of motion is solved and the Karhunen-Loeve expansion for the particle velocity is derived. The mean-square velocity as obtained by the truncated Karhunen-Loeve expansion is compared with the exact solution. It is shown, as the number of terms in the series increases, the result approaches that of the exact solution asymptotically.

Copyright © 1993 by The American Society of Mechanical Engineers
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