Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

Stochastic Manifolds for Nonlinear SPDEs II

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mickaël D. Chekroun, Honghu Liu, Shouhong Wang ISBN: 9783319125206
Publisher: Springer International Publishing Publication: December 23, 2014
Imprint: Springer Language: English
Author: Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
ISBN: 9783319125206
Publisher: Springer International Publishing
Publication: December 23, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Engineering Mathematics II by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Entrepreneurial Universities by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Herpes Zoster: Postherpetic Neuralgia and Other Complications by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Italian Motherhood on Screen by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Doping of Carbon Nanotubes by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Planning and Decision Making for Aerial Robots by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Chinese Water Systems by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book A Casebook in Interprofessional Ethics by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Postcolonial Reconstruction: A Sociological Reading of Octavio Paz by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book My 10 Strategies for Integrative Coaching by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book AI Injected e-Learning by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Information Technology in Environmental Engineering by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Knowledge Discovery, Knowledge Engineering and Knowledge Management by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book Recent Trends in Information and Communication Technology by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Cover of the book The Philosophy of Geo-Ontologies by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy