Approximation of Stochastic Invariant Manifolds
Shouhong Wang, Honghu Liu, Mickaël D. Chekroun
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
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.
Kundenbewertungen
Stochastic Invariant Manifolds, Stochastic Partial Differential Equations, ordinary differential equations, partial differential equations, Weak Non-Resonance Conditions, Leading-Order Taylor Approximations, 37L65,37D10,37L25,35B42,37L10,37L55., Lyapunov-Perron Integrals