Approximation of Stochastic Invariant Manifolds
Stochastic Manifolds for Nonlinear SPDEs I
Authors: Chekroun, Mickaël D., Liu, Honghu, Wang, Shouhong
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- About this book
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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.
- Reviews
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“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)
- Table of contents (7 chapters)
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General Introduction
Pages 1-7
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Stochastic Invariant Manifolds: Background and Main Contributions
Pages 9-12
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Preliminaries
Pages 13-27
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Existence and Attraction Properties of Global Stochastic Invariant Manifolds
Pages 29-47
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Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds
Pages 49-59
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Table of contents (7 chapters)
- Download Preface 1 PDF (52.2 KB)
- Download Sample pages 2 PDF (97.6 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Approximation of Stochastic Invariant Manifolds
- Book Subtitle
- Stochastic Manifolds for Nonlinear SPDEs I
- Authors
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- Mickaël D. Chekroun
- Honghu Liu
- Shouhong Wang
- Series Title
- SpringerBriefs in Mathematics
- Copyright
- 2015
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s)
- eBook ISBN
- 978-3-319-12496-4
- DOI
- 10.1007/978-3-319-12496-4
- Softcover ISBN
- 978-3-319-12495-7
- Series ISSN
- 2191-8198
- Edition Number
- 1
- Number of Pages
- XV, 127
- Number of Illustrations
- 1 illustrations in colour
- Topics
