Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II

Resource Information

The work Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II represents a distinct intellectual or artistic creation found in University of Liverpool. This resource is a combination of several types including: Work, Language Material, Books.

Label

Stochastic parameterizing manifolds and non-markovian 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

Creator

• Chekroun, Mickaël D

Contributor

• Wang, Shouhong
• Wang, Shouhong
• Liu, Honghu
• Liu, Honghu

Author

• Wang, Shouhong
• Chekroun, Mickaël D
• Wang, Shouhong
• Liu, Honghu
• Liu, Honghu

Subject

• Stochastic partial differential equations -- Numerical solutions

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. 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

Member of

• SpringerBriefs in mathematics
• Online access with purchase: Springer

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,