Effective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises

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  • Author : Jinqiao Duan
  • Publisher : Elsevier
  • Pages : 282 pages
  • ISBN : 0128012692
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKEffective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations
  • Author : Jinqiao Duan,Wei WANG
  • Publisher : Elsevier
  • Release : 06 March 2014
GET THIS BOOKEffective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers

Numerical Methods for Stochastic Partial Differential Equations with White Noise

Numerical Methods for Stochastic Partial Differential Equations with White Noise
  • Author : Zhongqiang Zhang,George Em Karniadakis
  • Publisher : Springer
  • Release : 01 September 2017
GET THIS BOOKNumerical Methods for Stochastic Partial Differential Equations with White Noise

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven

Stochastic Pdes And Modelling Of Multiscale Complex System

Stochastic Pdes And Modelling Of Multiscale Complex System
  • Author : Wang Wei,Chen Xiaopeng,Lv Yan
  • Publisher : World Scientific
  • Release : 07 May 2019
GET THIS BOOKStochastic Pdes And Modelling Of Multiscale Complex System

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the

Approximation of Stochastic Invariant Manifolds

Approximation of Stochastic Invariant Manifolds
  • Author : Mickaël D. Chekroun,Honghu Liu,Shouhong Wang
  • Publisher : Springer
  • Release : 20 December 2014
GET THIS BOOKApproximation of Stochastic Invariant Manifolds

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

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
  • Author : Mickaël D. Chekroun,Honghu Liu,Shouhong Wang
  • Publisher : Springer
  • Release : 23 December 2014
GET THIS BOOKStochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

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

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA
  • Author : Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue
  • Publisher : CRC Press
  • Release : 07 December 2018
GET THIS BOOKAdvanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and

Stochastic Ferromagnetism

Stochastic Ferromagnetism
  • Author : Lubomir Banas,Zdzislaw Brzezniak,Mikhail Neklyudov,Andreas Prohl
  • Publisher : Walter de Gruyter
  • Release : 18 December 2013
GET THIS BOOKStochastic Ferromagnetism

This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak

A Minicourse on Stochastic Partial Differential Equations

A Minicourse on Stochastic Partial Differential Equations
  • Author : Robert C. Dalang,Carl Mueller,Yimin Xiao,David Nualart
  • Publisher : Springer Science & Business Media
  • Release : 14 April 2021
GET THIS BOOKA Minicourse on Stochastic Partial Differential Equations

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

Partial Differential Equations

Partial Differential Equations
  • Author : Walter A. Strauss
  • Publisher : John Wiley & Sons
  • Release : 21 December 2007
GET THIS BOOKPartial Differential Equations

Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more. Rigorous pedagogical

Computational Partial Differential Equations

Computational Partial Differential Equations
  • Author : Hans Petter Langtangen
  • Publisher : Springer Science & Business Media
  • Release : 17 April 2013
GET THIS BOOKComputational Partial Differential Equations

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat

Stochastic Partial Differential Equations

Stochastic Partial Differential Equations
  • Author : Helge Holden,Bernt Oksendal,Jan Uboe,Tusheng Zhang
  • Publisher : Springer Science & Business Media
  • Release : 01 December 2013
GET THIS BOOKStochastic Partial Differential Equations

This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where

An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations
  • Author : Lawrence C. Evans
  • Publisher : American Mathematical Soc.
  • Release : 11 December 2012
GET THIS BOOKAn Introduction to Stochastic Differential Equations

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only