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SpringerBriefs in Mathematics

Approximation of Stochastic Invariant Manifolds

Stochastic Manifolds for Nonlinear SPDEs I

Authors: Chekroun, Mickaël D., Liu, Honghu, Wang, Shouhong

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  • ISBN 978-3-319-12496-4
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About this book

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

“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)

Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-12496-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-12495-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Approximation of Stochastic Invariant Manifolds
Book Subtitle
Stochastic Manifolds for Nonlinear SPDEs I
Authors
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