  The BBGKY hierarchy of equations for a particle interacting with an ideal gas
is investigated. Principal properties of its solutions are disclosed, as exact
identities which connect probability distribution of path of the particle, its
derivatives in respect to gas density and irreducible many-particle
correlations between gas molecules and the path. They show that all the
correlations always give equally important contributions to evolution of the
path distribution, and therefore the exact theory does not reduce to the
classical kinetics even at arbitrary small gas density.
