Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations Stochastic Manifolds for Nonlinear SPDEs II /
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)...
| Published in: | Springer eBooks |
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| Main Authors: | , , |
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Series: | SpringerBriefs in Mathematics,
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1007/978-3-319-12520-6 Перейти в каталог НБ ТГУ |
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| 100 | 1 | |a Chekroun, Mickaël D. |e author. |9 464606 | |
| 245 | 1 | 0 | |a Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations |h electronic resource |b Stochastic Manifolds for Nonlinear SPDEs II / |c by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang. |
| 260 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. |9 742221 | ||
| 300 | |a XVII, 129 p. 12 illus., 11 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8198 | |
| 505 | 0 | |a General Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index. | |
| 520 | |a 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. | ||
| 650 | 0 | |a mathematics. |9 566183 | |
| 650 | 0 | |a Dynamics. |9 460472 | |
| 650 | 0 | |a Ergodic theory. |9 461180 | |
| 650 | 0 | |a Differential Equations. |9 303496 | |
| 650 | 0 | |a Partial Differential Equations. |9 303602 | |
| 650 | 0 | |a Probabilities. |9 295556 | |
| 650 | 1 | 4 | |a Mathematics. |9 566184 |
| 650 | 2 | 4 | |a Partial Differential Equations. |9 303602 |
| 650 | 2 | 4 | |a Dynamical Systems and Ergodic Theory. |9 303500 |
| 650 | 2 | 4 | |a Probability Theory and Stochastic Processes. |9 303734 |
| 650 | 2 | 4 | |a Ordinary Differential Equations. |9 303501 |
| 700 | 1 | |a Liu, Honghu. |e author. |9 464607 | |
| 700 | 1 | |a Wang, Shouhong. |e author. |9 446369 | |
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| 912 | |a ZDB-2-SMA | ||
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