Special Session 53: Infinite dimensional stochastic systems and applications
Contents
Stochastic center manifolds theory are crucial in modelling the dynamical behavior of complex systems under stochastic influences. The multiplicative ergodic theorem is an important concept for random dynamical systems. 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.