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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

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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Series Title
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Call Number
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Publisher
London : Springer.,
Collation
-
Language
English
ISBN/ISSN
978-3-319-12520-6
Classification
NONE
Content Type
tactile text
Media Type
computer
Carrier Type
online resource
Edition
-
Subject(s)
Mathematics
Specific Detail Info
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Statement of Responsibility
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Cataloger
Jemadi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-12520-6.pdf?pdf=button
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