Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II /

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)...

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Detalhes bibliográficos
Main Authors: Chekroun, Mickaël D. (Author), Liu, Honghu (Author), Wang, Shouhong (Author)
Autor Corporativo: SpringerLink (Online service)
Formato: livro electrónico
Idioma:English
Publicado em: Cham : Springer International Publishing : Imprint: Springer, 2015.
Colecção:SpringerBriefs in Mathematics,
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Descrição
Resumo: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.
Descrição Física:1 online resource (xvii, 129 pages) 12 illustrations, 11 illustrations in color
ISBN:9783319125206
ISSN:2191-8198