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Mickaël D. Chekroun & Honghu Liu 
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations 
Stochastic Manifolds for Nonlinear SPDEs II

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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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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.
Língua Inglês ● Formato PDF ● Páginas 129 ● ISBN 9783319125206 ● Tamanho do arquivo 4.8 MB ● Editora Springer International Publishing ● Cidade Cham ● País CH ● Publicado 2014 ● Carregável 24 meses ● Moeda EUR ● ID 5023417 ● Proteção contra cópia DRM social

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