  Stochastic center manifolds theory are crucial in modelling the dynamical
behavior of complex systems under stochastic influences. A multiplicative
ergodic theorem on Hilbert space is proved to be satisfied to the exponential
trichotomy condition. Then the existence of stochastic center manifolds for
infinite dimensional random dynamical systems is shown under the assumption of
exponential trichotomy. The theory provides a support for the discretisations
of nonlinear stochastic partial differential equations with space-time white
noise.
