Brownian Motions

Brownian Motion in a Force Field

Consider the following Langevin equation:

(18)

where

(19)

is a conservative force field. The corresponding Fokker-Planck equation for the transition probability density function is given as:

(20)

The stationary solution to (20) is given by

(21)

Using (19), we find

(22)

For a gravitational force field,

(23)

and

(24)