  Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of
molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio
$m/M$. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
$(m/M)^2$ and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented.
