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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| Main Authors: | , , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Series: | SpringerBriefs in Mathematics,
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| Subjects: | |
| Online Access: | Click here to view the full text content |
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| Summary: | 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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| Physical Description: | 1 online resource (xvii, 129 pages) 12 illustrations, 11 illustrations in color |
| ISBN: | 9783319125206 |
| ISSN: | 2191-8198 |