Mickaël D. Chekroun & Honghu Liu 
Approximation of Stochastic Invariant Manifolds 
Stochastic Manifolds for Nonlinear SPDEs I

General Introduction.- Stochastic Invariant Manifolds: Background and Main Contributions.- Preliminaries.- Stochastic Evolution Equations.- Random Dynamical Systems.- Cohomologous Cocycles and Random Evolution Equations .- Linearized Stochastic Flow and Related Estimates .- Existence and Attraction Properties of Global Stochastic Invariant Manifolds .- Existence and Smoothness of Global Stochastic Invariant Manifolds.- Asymptotic Completeness of Stochastic Invariant Manifolds.- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds.- Local Stochastic Critical Manifolds: Existence and Approximation Formulas .- Standing Hypotheses.- Existence of Local Stochastic Critical Manifolds .- Approximation of Local Stochastic Critical Manifolds.- Proofs of Theorem 6.1 and Corollary 6.1.- Approximation of Stochastic Hyperbolic Invariant Manifolds .- A Classical and Mild Solutions of the Transformed RPDE .- B Proof of Theorem 4.1.- References.