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Parameterizing Manifolds and Non-Markovian Reduced Equations

MickaŽl D. Chekroun

Editore: Springer-Verlag Gmbh Feb 2015, 2015
ISBN 10: 3319125192 / ISBN 13: 9783319125190
Nuovi / Taschenbuch / Quantitŗ: 1
Da Rhein-Team Lörrach Ivano Narducci e.K. (Lörrach, Germania)
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Titolo: Parameterizing Manifolds and Non-Markovian ...

Casa editrice: Springer-Verlag Gmbh Feb 2015

Data di pubblicazione: 2015

Legatura: Taschenbuch

Condizione libro: Neu

Descrizione:

Neuware - 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. 129 pp. Englisch. Codice inventario libreria 9783319125190

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Riassunto: 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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Libreria: Rhein-Team Lörrach Ivano Narducci e.K.
Indirizzo: Lörrach, Germania

Libreria AbeBooks dal: 11 gennaio 2012
Valutazione libreria: 5 stelle

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