Approximation of Stochastic Invariant Manifolds
This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov...
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2015
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oai:scholar.dlu.edu.vn:DLU123456789-578052023-11-11T05:52:56Z Approximation of Stochastic Invariant Manifolds Chekroun, Mickaël D Liu, Honghu Wang Mathematics Calcul Mathematical Analysis This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems. 2015-08-28T01:54:17Z 2015-08-28T01:54:17Z 2015 Book 978-3-319-12496-4 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57805 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Mathematics Calcul Mathematical Analysis |
| spellingShingle |
Mathematics Calcul Mathematical Analysis Chekroun, Mickaël D Liu, Honghu Wang Approximation of Stochastic Invariant Manifolds |
| description |
This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems. |
| format |
Book |
| author |
Chekroun, Mickaël D Liu, Honghu Wang |
| author_facet |
Chekroun, Mickaël D Liu, Honghu Wang |
| author_sort |
Chekroun, Mickaël D |
| title |
Approximation of Stochastic Invariant Manifolds |
| title_short |
Approximation of Stochastic Invariant Manifolds |
| title_full |
Approximation of Stochastic Invariant Manifolds |
| title_fullStr |
Approximation of Stochastic Invariant Manifolds |
| title_full_unstemmed |
Approximation of Stochastic Invariant Manifolds |
| title_sort |
approximation of stochastic invariant manifolds |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57805 |
| _version_ |
1782549796129603584 |