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

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Abstract
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.