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Approximation of stochastic invarian...

Chekroun, Mickael D.

Approximation of stochastic invariant manifoldsstochastic manifolds for nonlinear SPDEs I /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Approximation of stochastic invariant manifoldsby Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
Reminder of title:	stochastic manifolds for nonlinear SPDEs I /
Author:	Chekroun, Mickael D.
other author:	Liu, Honghu.
Published:	Cham :Springer International Publishing :2015.
Description:	xv, 127 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Stochastic partial differential equations.
Online resource:	http://dx.doi.org/10.1007/978-3-319-12496-4
ISBN:	9783319124964 (electronic bk.)

Approximation of stochastic invariant manifoldsstochastic manifolds for nonlinear SPDEs I /
Chekroun, Mickael D.

Approximation of stochastic invariant manifoldsstochastic manifolds for nonlinear SPDEs I /[electronic resource] :by Mickael D. Chekroun, Honghu Liu, Shouhong Wang. - Cham :Springer International Publishing :2015. - xv, 127 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

General Introduction -- Stochastic Invariant Manifolds: Background and Main Contributions -- Preliminaries -- Stochastic Evolution Equations -- Random Dynamical Systems -- Cohomologous Cocycles and Random Evolution Equations -- Linearized Stochastic Flow and Related Estimates -- Existence and Attraction Properties of Global Stochastic Invariant Manifolds -- Existence and Smoothness of Global Stochastic Invariant Manifolds -- Asymptotic Completeness of Stochastic Invariant Manifolds -- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds -- Local Stochastic Critical Manifolds: Existence and Approximation Formulas -- Standing Hypotheses -- Existence of Local Stochastic Critical Manifolds -- Approximation of Local Stochastic Critical Manifolds -- Proofs of Theorem 6.1 and Corollary 6.1 -- Approximation of Stochastic Hyperbolic Invariant Manifolds -- A Classical and Mild Solutions of the Transformed RPDE -- B Proof of Theorem 4.1 -- References.

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.

ISBN: 9783319124964 (electronic bk.)

Standard No.: 10.1007/978-3-319-12496-4doiSubjects--Topical Terms:

199002
Stochastic partial differential equations.

LC Class. No.: QA274.25

Dewey Class. No.: 515.353

Approximation of stochastic invariant manifoldsstochastic manifolds for nonlinear SPDEs I /
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100 1 $a Chekroun, Mickael D. $3 713099
245 1 0 $a Approximation of stochastic invariant manifolds $h [electronic resource] : $b stochastic manifolds for nonlinear SPDEs I / $c by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xv, 127 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a General Introduction -- Stochastic Invariant Manifolds: Background and Main Contributions -- Preliminaries -- Stochastic Evolution Equations -- Random Dynamical Systems -- Cohomologous Cocycles and Random Evolution Equations -- Linearized Stochastic Flow and Related Estimates -- Existence and Attraction Properties of Global Stochastic Invariant Manifolds -- Existence and Smoothness of Global Stochastic Invariant Manifolds -- Asymptotic Completeness of Stochastic Invariant Manifolds -- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds -- Local Stochastic Critical Manifolds: Existence and Approximation Formulas -- Standing Hypotheses -- Existence of Local Stochastic Critical Manifolds -- Approximation of Local Stochastic Critical Manifolds -- Proofs of Theorem 6.1 and Corollary 6.1 -- Approximation of Stochastic Hyperbolic Invariant Manifolds -- A Classical and Mild Solutions of the Transformed RPDE -- B Proof of Theorem 4.1 -- References.
520 $a 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.
650 0 $a Stochastic partial differential equations. $3 199002
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Ordinary Differential Equations. $3 273778
700 1 $a Liu, Honghu. $3 713100
700 1 $a Wang, Shouhong. $3 266558
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-12496-4
950 $a Mathematics and Statistics (Springer-11649)