Approximation of Stochastic Invariant Manifolds

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.
Includes supplementary material: sn.pub/extras

Autor*in

Mickaël D. Chekroun

Themen in »Approximation of Stochastic Invariant Manifolds«

37L65,37D10,37L25,35B42,37L10,37L55. Leading-Order Taylor Approximations Lyapunov-Perron Integrals Stochastic Invariant Manifolds Stochastic Partial Differential Equations Weak Non-Resonance Conditions partial differential equations ordinary differential equations

Stimmen zu »Approximation of Stochastic Invariant Manifolds«

“The book under review is the first in a two-volume series and deals with approximation of stochastic manifolds that are invariant for dynamics of a parabolic Stratonovich SPDE driven by a one-dimensional Wiener process. … The book is aimed at readers interested in stochastic partial differential equations and random dynamical systems.” (Martin Ondreját, zbMATH 1319.60002, 2015)

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