Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

Name: Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
SKU: 22845133
Price: 135.99 AUD
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Stochastic Manifolds for Nonlinear SPDEs II

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Paperback / softback

Series:

Springerbriefs in Mathematics

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Description

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.

Release date Australia

January 14th, 2015

Author

Audience

Postgraduate, Research & Scholarly

Illustrations

11 Illustrations, color; 1 Illustrations, black and white; XVII, 129 p. 12 illus., 11 illus. in color.

Pages

129

Series

Springerbriefs in Mathematics

Dimensions

155x235x8

ISBN-13

9783319125190

Product ID

22845133

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