  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 via
instantaneous collisions. Using the van Kampen method of expansion of the
master equation, non-linear corrections to the Fokker-Planck equation are
obtained up to sixth order in the small parameter 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.
