Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations Stochastic Manifolds for Nonlinear SPDEs II
Aus der Reihe
SpringerBriefs in Mathematics
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Sprache:Englisch
Fr. 73.90
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
14.01.2015
Abbildungen
XVII, 12 illus., 11 illus. in color., schwarz-weiss Illustrationen, farbige Illustrationen
Verlag
SpringerSeitenzahl
129
Maße (L/B/H)
23.5/15.5/0.9 cm
Gewicht
248 g
Auflage
2015
Sprache
Englisch
ISBN
978-3-319-12519-0
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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