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Approximation of Stochastic Invariant Manifolds
Mickaël D. ChekrounHonghu LiuShouhong Wang
其他書名
Stochastic Manifolds for Nonlinear SPDEs I
出版Springer, 2014-12-20
主題Mathematics / Mathematical AnalysisMathematics / Differential Equations / GeneralMathematics / Probability & Statistics / GeneralMathematics / Linear & Nonlinear Programming
ISBN331912496X9783319124964
URLhttp://books.google.com.hk/books?id=1-7nBQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.