# Effective Dynamics of Stochastic Partial Differential Equations

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## Effective Dynamics of Stochastic Partial Differential Equations

Author | : Jinqiao Duan,Wei WANG |

Publsiher | : Elsevier |

Total Pages | : 282 |

Release | : 2014-03-06 |

ISBN 10 | : 0128012692 |

ISBN 13 | : 9780128012697 |

Language | : EN, FR, DE, ES & NL |

**Effective Dynamics of Stochastic Partial Differential Equations Book Review:**

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

## Effective Dynamics of Stochastic Partial Differential Equations

Author | : Jinqiao Duan,Wei Wang |

Publsiher | : Elsevier |

Total Pages | : 284 |

Release | : 2017-11-13 |

ISBN 10 | : 9780128102510 |

ISBN 13 | : 0128102519 |

Language | : EN, FR, DE, ES & NL |

**Effective Dynamics of Stochastic Partial Differential Equations Book Review:**

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 uncertaintyAccessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equationsSolutions or hints to all Exercises"

## An Introduction to Stochastic Dynamics

Author | : Jinqiao Duan |

Publsiher | : Cambridge University Press |

Total Pages | : 307 |

Release | : 2015-04-13 |

ISBN 10 | : 1107075394 |

ISBN 13 | : 9781107075399 |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Stochastic Dynamics Book Review:**

An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

## Numerical Methods for Stochastic Partial Differential Equations with White Noise

Author | : Zhongqiang Zhang,George Em Karniadakis |

Publsiher | : Springer |

Total Pages | : 394 |

Release | : 2017-09-01 |

ISBN 10 | : 3319575112 |

ISBN 13 | : 9783319575117 |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods for Stochastic Partial Differential Equations with White Noise Book Review:**

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 by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

## Stochastic Partial Differential Equations

Author | : Helge Holden,Bernt Oksendal,Jan Uboe,Tusheng Zhang |

Publsiher | : Springer Science & Business Media |

Total Pages | : 231 |

Release | : 2013-12-01 |

ISBN 10 | : 1468492152 |

ISBN 13 | : 9781468492156 |

Language | : EN, FR, DE, ES & NL |

**Stochastic Partial Differential Equations Book Review:**

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 some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.

## Stochastic Partial Differential Equations

Author | : Alison Etheridge,N. J. Hitchin |

Publsiher | : Cambridge University Press |

Total Pages | : 337 |

Release | : 1995-07-13 |

ISBN 10 | : 9780521483193 |

ISBN 13 | : 0521483190 |

Language | : EN, FR, DE, ES & NL |

**Stochastic Partial Differential Equations Book Review:**

Consists of papers given at the ICMS meeting held in 1994 on this topic, and brings together some of the world's best known authorities on stochastic partial differential equations.

## Stochastic Ferromagnetism

Author | : Lubomir Banas,Zdzislaw Brzezniak,Mikhail Neklyudov,Andreas Prohl |

Publsiher | : Walter de Gruyter |

Total Pages | : 248 |

Release | : 2013-12-18 |

ISBN 10 | : 3110307103 |

ISBN 13 | : 9783110307108 |

Language | : EN, FR, DE, ES & NL |

**Stochastic Ferromagnetism Book Review:**

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 martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.

## A Minicourse on Stochastic Partial Differential Equations

Author | : Robert C. Dalang,Carl Mueller,Yimin Xiao,David Nualart |

Publsiher | : Springer Science & Business Media |

Total Pages | : 216 |

Release | : 2009 |

ISBN 10 | : 3540859934 |

ISBN 13 | : 9783540859932 |

Language | : EN, FR, DE, ES & NL |

**A Minicourse on Stochastic Partial Differential Equations Book Review:**

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.

## 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 |

Publsiher | : CRC Press |

Total Pages | : 284 |

Release | : 2018-12-07 |

ISBN 10 | : 0429629850 |

ISBN 13 | : 9780429629853 |

Language | : EN, FR, DE, ES & NL |

**Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA Book Review:**

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 real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

## Blow up Theories for Semilinear Parabolic Equations

Author | : Bei Hu |

Publsiher | : Springer Science & Business Media |

Total Pages | : 127 |

Release | : 2011-03-23 |

ISBN 10 | : 3642184596 |

ISBN 13 | : 9783642184598 |

Language | : EN, FR, DE, ES & NL |

**Blow up Theories for Semilinear Parabolic Equations Book Review:**

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

## Stochastic Partial Differential Equations and Applications

Author | : Giuseppe Da Prato,Luciano Tubaro |

Publsiher | : Springer |

Total Pages | : 264 |

Release | : 2006-11-15 |

ISBN 10 | : 3540474080 |

ISBN 13 | : 9783540474081 |

Language | : EN, FR, DE, ES & NL |

**Stochastic Partial Differential Equations and Applications Book Review:**

## SIAM Journal on Scientific Computing

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2004 |

ISBN 10 | : |

ISBN 13 | : UVA:X006170534 |

Language | : EN, FR, DE, ES & NL |

**SIAM Journal on Scientific Computing Book Review:**

## Wave Propagation and Time Reversal in Randomly Layered Media

Author | : Jean-Pierre Fouque,Josselin Garnier,G. Papanicolaou,Knut Solna |

Publsiher | : Springer Science & Business Media |

Total Pages | : 612 |

Release | : 2007-06-30 |

ISBN 10 | : 0387498087 |

ISBN 13 | : 9780387498089 |

Language | : EN, FR, DE, ES & NL |

**Wave Propagation and Time Reversal in Randomly Layered Media Book Review:**

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter.

## Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

Author | : Carlos A. Braumann |

Publsiher | : John Wiley & Sons |

Total Pages | : 304 |

Release | : 2019-03-08 |

ISBN 10 | : 1119166071 |

ISBN 13 | : 9781119166078 |

Language | : EN, FR, DE, ES & NL |

**Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance Book Review:**

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

## Free Energy Computations

Author | : Tony Lelivre,Gabriel Stoltz,Mathias Rousset |

Publsiher | : World Scientific |

Total Pages | : 458 |

Release | : 2010 |

ISBN 10 | : 1848162472 |

ISBN 13 | : 9781848162471 |

Language | : EN, FR, DE, ES & NL |

**Free Energy Computations Book Review:**

This monograph provides a general introduction to advanced computational methods for free energy calculations, from the systematic and rigorous point of view of applied mathematics. Free energy calculations in molecular dynamics have become an outstanding and increasingly broad computational field in physics, chemistry and molecular biology within the past few years, by making possible the analysis of complex molecular systems. This work proposes a new, general and rigorous presentation, intended both for practitioners interested in a mathematical treatment, and for applied mathematicians interested in molecular dynamics.

## Partial Differential Equations

Author | : Walter A. Strauss |

Publsiher | : John Wiley & Sons |

Total Pages | : 464 |

Release | : 2007-12-21 |

ISBN 10 | : 0470054565 |

ISBN 13 | : 9780470054567 |

Language | : EN, FR, DE, ES & NL |

**Partial Differential Equations Book Review:**

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 tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

## An Introduction to Stochastic Differential Equations

Author | : Lawrence C. Evans |

Publsiher | : American Mathematical Soc. |

Total Pages | : 151 |

Release | : 2012-12-11 |

ISBN 10 | : 1470410540 |

ISBN 13 | : 9781470410544 |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Stochastic Differential Equations Book Review:**

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 a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

## Waves and Mean Flows

Author | : Oliver Bühler |

Publsiher | : Cambridge University Press |

Total Pages | : 341 |

Release | : 2009-08-20 |

ISBN 10 | : 0521866367 |

ISBN 13 | : 9780521866361 |

Language | : EN, FR, DE, ES & NL |

**Waves and Mean Flows Book Review:**

A modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. It can be used as a fundamental reference, a course text, or by geophysicists and physicists needing an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.

## Perspectives in Mathematical Sciences

Author | : Yisong Yang,Xinchu Fu,Jinqiao Duan |

Publsiher | : World Scientific |

Total Pages | : 354 |

Release | : 2010 |

ISBN 10 | : 9814289310 |

ISBN 13 | : 9789814289313 |

Language | : EN, FR, DE, ES & NL |

**Perspectives in Mathematical Sciences Book Review:**

Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences. This is a review volume on some timely and interesting topics in applied mathematical sciences. It reviews new developments and presents some future research directions in these topics. The chapters are written by reknowned experts in these fields. The volume is written with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subject. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. An entire chapter will be devoted to his achievements. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.

## Differential Equations for Engineers

Author | : Wei-Chau Xie |

Publsiher | : Cambridge University Press |

Total Pages | : 329 |

Release | : 2010-04-26 |

ISBN 10 | : 1139488163 |

ISBN 13 | : 9781139488167 |

Language | : EN, FR, DE, ES & NL |

**Differential Equations for Engineers Book Review:**

Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.