On the theory of Brownian motion. VI. Asymptotic solution of a retarded Fokker-Planck equation

The solution of a retarded one-dimensional Fokker-Planck equation is expressed in terms of a contour integral. This integral is evaluated asymptotically for two forms of the force correlation function: (a) a delta function (classical case-no retardation) and (b) a t−3/2 fall off for long times. Solutions are expressed in terms of known functions. It is indicated how this technique can be extended to the three-dimensional case, and the appropriate Green's functions are displayed.