  Random invariant manifolds often provide geometric structures for
understanding stochastic dynamics. In this paper, a dynamical approximation
estimate is derived for a class of stochastic partial differential equations,
by showing that the random invariant manifold is almost surely asymptotically
complete. The asymptotic dynamical behavior is thus described by a stochastic
ordinary differential system on the random invariant manifold, under suitable
conditions. As an application, stationary states (invariant measures) is
considered for one example of stochastic partial differential equations.
