| The study of the long time behavior of systems with time scale separation is considerably facilitated if the fast degrees of freedom can be eliminated without affecting the slow dynamics. By applying projection operator techniques we show that in chaotic Hamiltonian systems the fast subsystem can be replaced by a suitable stochastic process so that the slow motion is effectively described by a Fokker--Planck equation where the interplay of viscous damping and diffusion conserves the total energy and ensures the correct long time behavior. The accuracy and efficiency of this approach is verified by a numerical investigation of suitable model systems. |