Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I - SpringerBriefs in Mathematics (Paperback)
  • Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I - SpringerBriefs in Mathematics (Paperback)
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Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I - SpringerBriefs in Mathematics (Paperback)

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Paperback 127 Pages / Published: 13/01/2015
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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.

Publisher: Springer International Publishing AG
ISBN: 9783319124957
Number of pages: 127
Weight: 2292 g
Dimensions: 235 x 155 x 8 mm
Edition: 2015 ed.


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 Ondrejat, zbMATH 1319.60002, 2015)

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