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Item Details
| Title:
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STOCHASTIC PARAMETERIZING MANIFOLDS AND NON-MARKOVIAN REDUCED EQUATIONS
STOCHASTIC MANIFOLDS FOR NONLINEAR SPDES II |
| By: |
Mickael D. Chekroun, Shouhong Wang, Honghu Liu |
| Format: |
Paperback |
| List price:
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£49.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3319125192 |
| ISBN 13: |
9783319125190 |
| Publisher: |
SPRINGER INTERNATIONAL PUBLISHING AG |
| Pub. date: |
1 December, 2014 |
| Edition: |
2015 ed. |
| Series: |
SpringerBriefs in Mathematics |
| Pages: |
129 |
| Synopsis: |
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. |
| Illustrations: |
11 Illustrations, color; 1 Illustrations, black and white; XVII, 129 p. 12 |
| Publication: |
Switzerland |
| Imprint: |
Springer International Publishing AG |
| Returns: |
Returnable |
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