Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II
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The work Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II
Resource Information
The work Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II
 Title remainder
 stochastic manifolds for nonlinear SPDEs II
 Statement of responsibility
 Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
 Subject

 Mathematics
 Probability Theory and Stochastic Processes
 Ordinary Differential Equations
 Electronic books
 Differential calculus & equations
 MATHEMATICS  Mathematical Analysis
 Stochastic partial differential equations  Numerical solutions
 Stochastic partial differential equations  Numerical solutions
 Probability & statistics
 Partial Differential Equations
 Nonlinear science
 MATHEMATICS  Calculus
 Dynamical Systems and Ergodic Theory
 Language
 eng
 Summary
 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. Backwardforward 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 timehistory of the modes with low wave numbers. NonMarkovian 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 Burgerstype equation
 Cataloging source
 N$T
 Dewey number
 515/.353
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA274.25
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SpringerBriefs in Mathematics,
Context
Context of Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs IIWork of
 Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
 Stochastic parameterizing manifolds and nonmarkovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
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