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.

This content is only available via PDF.
You do not currently have access to this content.