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Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I

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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.

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Series Title

SpringerBriefs in Mathematics

Call Number

519 CHE a

Publisher

Cham, Switzerland : Springer Cham., 2015

Collation

XV, 127

Language

English

ISBN/ISSN

978-3-319-12496-4

Classification

519

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

partial differential equations
Probability Theory and Stochastic Processes

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Statement of Responsibility

Mickaël D. Chekroun, Honghu Liu, Shouhong Wang

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Cataloger

umi

Source

https://link.springer.com/book/10.1007/978-3-319-12496-4

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