Longtime behaviour of stochastic Hamiltonian systems: The multidimensionalcase

Hamiltonian systems perturbed by a white noise force are discussed in sever al dimensions. By using an appropriate scaling of the stochastic force a co nvergence theorem for the invariants of the deterministic motion is proved. This corresponds to convergence of the system to a stationary distribution . Especially motion in a central force field is considered; the energy and angular momentum processes are investigated.