ASYMPTOTIC ANALYSIS OF THE FOKKER-PLANCK EQUATION RELATED TO BROWNIAN MOTION

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Abstract
In this paper we apply the modified Chapman-Enskog expansion procedure to find the asymptotic solution of the Fokker-Planck equation related to Brownian motion. We prove that the asymptotic solution is defined by the diffusion equation and show that the difference between the exact and asymptotic solutions is of order ε2 where 1/ε is related to the magnitude of the collision operator.