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 Boston University 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 Boston University 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
 by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
 Subject

 Probability Theory and Stochastic Processes
 Differential Equations
 Ordinary Differential Equations
 Differentiable dynamical systems
 Mathematics
 Mathematics
 Distribution (Probability theory)
 Distribution (Probability theory)
 Differential Equations
 Differential Equations
 Electronic resources
 Mathematics
 Distribution (Probability theory)
 Partial Differential Equations
 Differentiable dynamical systems
 Differential equations, partial
 Dynamical Systems and Ergodic Theory
 Differential equations, partial
 Differentiable dynamical systems
 Differential equations, partial
 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
 Image bit depth
 0
 LC call number
 QA370380
 Literary form
 non fiction
 Series statement
 SpringerBriefs in Mathematics,
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