Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I - Couverture souple

Livre 52 sur 155: SpringerBriefs in Mathematics

Chekroun, Mickaël D. D.; Liu, Honghu; Wang, Shouhong

 
9783319124957: Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I

Synopsis

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.

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