Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations - Stochastic Manifolds for Nonlinear SPDEs II (Paperback, 2015 ed.)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	SpringerBriefs in Mathematics
Release date:	December 2014
First published:	2015
Authors:	Mickael D. Chekroun • Honghu Liu • Shouhong Wang
Dimensions:	235 x 155 x 8mm (L x W x T)
Format:	Paperback
Pages:	129
Edition:	2015 ed.
ISBN-13:	978-3-319-12519-0
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	3-319-12519-2
Barcode:	9783319125190

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