  The rigorous approach to the description of the kinetic evolution of a
many-particle system composed of a trace hard sphere and an environment of
finitely many hard spheres is developed. We prove that the evolution of states
of a trace hard sphere in an environment can be described within the framework
of the marginal distribution function governed by the generalized Fokker --
Planck kinetic equation and an infinite sequence of the explicitly defined
functionals of this function.
