Title: Approximation of Stochastic Invariant Manifolds
Description: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations  take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Subjects: Mathematics, Differentiable dynamical systems, Differential Equations, Differential equations, partial, Distribution (Probability theory), Dynamical Systems and Ergodic Theory, Partial Differential Equations, Probability Theory and Stochastic Processes, Ordinary Differential Equations