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Stochastic parameterizing manifolds ...

Chekroun, Mickael D.

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Stochastic parameterizing manifolds and non-markovian reduced equations = Stochastic Manifolds for Nonlinear SPDEs II /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stochastic parameterizing manifolds and non-markovian reduced equations/ by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
Reminder of title:	Stochastic Manifolds for Nonlinear SPDEs II /
Author:	Chekroun, Mickael D.
other author:	Liu, Honghu.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xvii, 129 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	General Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index.
Contained By:	Springer eBooks
Subject:	Stochastic partial differential equations - Numerical solutions. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-12520-6
ISBN:	9783319125206 (electronic bk.)

Stochastic parameterizing manifolds and non-markovian reduced equations = Stochastic Manifolds for Nonlinear SPDEs II /
Chekroun, Mickael D.

Stochastic parameterizing manifolds and non-markovian reduced equationsStochastic Manifolds for Nonlinear SPDEs II /[electronic resource] :by Mickael D. Chekroun, Honghu Liu, Shouhong Wang. - Cham :Springer International Publishing :2015. - xvii, 129 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

General Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index.

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

ISBN: 9783319125206 (electronic bk.)

Standard No.: 10.1007/978-3-319-12520-6doiSubjects--Topical Terms:

816292
Stochastic partial differential equations
--Numerical solutions.

LC Class. No.: QA274.25

Dewey Class. No.: 515.353

Stochastic parameterizing manifolds and non-markovian reduced equations = Stochastic Manifolds for Nonlinear SPDEs II /
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100 1 $a Chekroun, Mickael D. $3 2133571
245 1 0 $a Stochastic parameterizing manifolds and non-markovian reduced equations $h [electronic resource] : $b Stochastic Manifolds for Nonlinear SPDEs II / $c by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xvii, 129 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a General Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index.
520 $a In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
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650 1 4 $a Mathematics. $3 515831
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650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Probability Theory and Stochastic Processes. $3 891080
650 2 4 $a Ordinary Differential Equations. $3 891264
700 1 $a Liu, Honghu. $3 2133572
700 1 $a Wang, Shouhong. $3 935654
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a SpringerBriefs in mathematics. $3 1566700
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