Brownian Motion in a Stellar System

The random motion of a star in phase space is examined using the autocorrelation function of the ran- dom force acting on the star. In this framework the long "memory" of weak forces leads to a divergent expression for the mean square velocity increment of the star. It is shown that this expression is equivalent to one obtained by summing independently the effects of complete encounters. A procedure of summing velocity increments is developed and extended to include distant encounters. The transition probability is found and is used to examine the validity of the Fokker-Planck equation