Approximation of Stochastic Invariant Manifolds
Author | : Mickaël D. Chekroun |
Publisher | : Springer |
Total Pages | : 136 |
Release | : 2014-12-20 |
ISBN-10 | : 9783319124964 |
ISBN-13 | : 331912496X |
Rating | : 4/5 (96X Downloads) |
Download or read book Approximation of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.