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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
Chekroun, Mickael D.; Wang, Shouhong; Liu, Honghu
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Description for Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
Paperback. Series: SpringerBriefs in Mathematics. Num Pages: 146 pages, 1 black & white illustrations, 11 colour illustrations, biography. BIC Classification: PBKJ; PBT; PBWR. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 8. Weight in Grams: 238.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2014
Publisher
Springer International Publishing AG Switzerland
Number of pages
146
Condition
New
Series
SpringerBriefs in Mathematics
Number of Pages
129
Place of Publication
Cham, Switzerland
ISBN
9783319125190
SKU
V9783319125190
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
Reviews for Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
“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)