On the higher order corrections to the Fokker-Planck equation

The Rayleigh model of nonlinear Brownian motion is revisited in which the heavy particle of mass M interacts with ideal gas molecules of mass m⪡M via instantaneous collisions. Using the van Kampen method of expansion of the master equation, nonlinear corrections to the Fokker-Planck equation are obtained up to sixth order in the small parameter λ=m/M, improving earlier results. The role and origin of non-Gaussian statistics of the random force in the corresponding Langevin equation are also discussed.