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Stochastic parameterizing manifolds ...

Chekroun, Mickael D.

Stochastic parameterizing manifolds and non-markovian reduced equations[electronic resource] :Stochastic Manifolds for Nonlinear SPDEs II /

レコード種別:	言語・文字資料 (印刷物) : 単行資料
[NT 15000414] null:	515.353
タイトル / 著者:	Stochastic parameterizing manifolds and non-markovian reduced equations : Stochastic Manifolds for Nonlinear SPDEs II // by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
著者:	Chekroun, Mickael D.
その他の著者:	Liu, Honghu.
出版された:	Cham : : Springer International Publishing :, 2015.
記述:	xvii, 129 p. : : ill. (some col.), digital ;; 24 cm.
含まれています:	Springer eBooks
主題:	Stochastic partial differential equations - Numerical solutions.
主題:	Mathematics.
主題:	Partial Differential Equations.
主題:	Dynamical Systems and Ergodic Theory.
主題:	Probability Theory and Stochastic Processes.
主題:	Ordinary Differential Equations.
国際標準図書番号 (ISBN) :	9783319125206 (electronic bk.)
国際標準図書番号 (ISBN) :	9783319125190 (paper)
[NT 15000228] null:	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.
[NT 15000229] null:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-12520-6

Stochastic parameterizing manifolds and non-markovian reduced equations[electronic resource] :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:

605622
Stochastic partial differential equations
--Numerical solutions.

LC Class. No.: QA274.25

Dewey Class. No.: 515.353

Stochastic parameterizing manifolds and non-markovian reduced equations[electronic resource] :Stochastic Manifolds for Nonlinear SPDEs II /
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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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