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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| Otros Autores: | , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing
2015.
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| Colección: | SpringerBriefs in Mathematics.
Springer eBooks. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32920404*spi |
| Sumario: | 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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| Descripción Física: | XVII, 129 p., 12 il., 11 il. col |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9783319125206 |
