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

Chekroun, Mickaël D. D.; Liu, Honghu; Wang, Shouhong

ISBN 10: 3319124951 / ISBN 13: 9783319124957

Editore: Springer, 2015

Print on Demand 127. Codice articolo 374914969

Riassunto:

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.

Recensione:

“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)

Dati bibliografici

Titolo: Approximation of Stochastic Invariant ...
Casa editrice: Springer
Data di pubblicazione: 2015
Legatura: Brossura
Condizione: New