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SpringerBriefs in Mathematics

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

Stochastic Manifolds for Nonlinear SPDEs II

Authors: Chekroun, Mickaël D., Liu, Honghu, Wang, Shouhong

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  • ISBN 978-3-319-12520-6
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About this book

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.

Reviews

“The monograph is well written and contains novel and important results for researchers in the field of analytical or numerical random dynamical systems and SPDEs. The clarity of presentation as well as the detailed list of references, makes it also appealing to research students as well as to newcomers to the field.” (Athanasios Yannacopoulos, zbMATH 1331.37009, 2016)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-12520-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-12519-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
Book Subtitle
Stochastic Manifolds for Nonlinear SPDEs II
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-12520-6
DOI
10.1007/978-3-319-12520-6
Softcover ISBN
978-3-319-12519-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XVII, 129
Number of Illustrations
1 b/w illustrations, 11 illustrations in colour
Topics