Approximation of Stochastic Invariant Manifolds :Stochastic Manifolds for Nonlinear SPDEs I - SpringerBriefs in Mathematics
Approximation of Stochastic Invariant Manifolds :Stochastic Manifolds for Nonlinear SPDEs I - SpringerBriefs in Mathematics
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Published:
13 January, 2015
paperback
Published:
13 January, 2015
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Description
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.
More Details
| Type | Book |
|---|---|
| ISBN13 | 9783319124957 |
| ISBN10 | 3319124951 |
| Number Of Pages | 127 |
| Item Weight | 1000 g |
| Publisher / Reseller | Springer International Publishing AG |
| Format | paperback |
| Edition | 2015 ed. |
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Media 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)