Three Classes Of Nonlinear Stochastic Partial Differential Equations
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Three Classes Of Nonlinear Stochastic Partial Differential Equations
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Author : Jie Xiong
language : en
Publisher: World Scientific
Release Date : 2013-05-06
Three Classes Of Nonlinear Stochastic Partial Differential Equations written by Jie Xiong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-06 with Mathematics categories.
The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.
A Concise Course On Stochastic Partial Differential Equations
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Author : Claudia Prévôt
language : en
Publisher: Springer
Release Date : 2007-05-26
A Concise Course On Stochastic Partial Differential Equations written by Claudia Prévôt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Numerical Methods For Stochastic Partial Differential Equations With White Noise
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Author : Zhongqiang Zhang
language : en
Publisher: Springer
Release Date : 2017-09-12
Numerical Methods For Stochastic Partial Differential Equations With White Noise written by Zhongqiang Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Mathematics categories.
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.
Nonlinear Partial Differential Equations
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Author : Mi-Ho Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30
Nonlinear Partial Differential Equations written by Mi-Ho Giga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Mathematics categories.
This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
Probability And Partial Differential Equations In Modern Applied Mathematics
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Author : Edward C. Waymire
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-14
Probability And Partial Differential Equations In Modern Applied Mathematics written by Edward C. Waymire and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-14 with Mathematics categories.
"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Financial Modeling
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Author : Stephane Crepey
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Financial Modeling written by Stephane Crepey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Computers categories.
Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance
Backward Stochastic Differential Equations
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Author : N El Karoui
language : en
Publisher: CRC Press
Release Date : 1997-01-17
Backward Stochastic Differential Equations written by N El Karoui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-17 with Mathematics categories.
This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Composite Media And Homogenization Theory
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Author : Gianni Dal Maso
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Composite Media And Homogenization Theory written by Gianni Dal Maso and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the Proceedings of the Workshop on Composite Media and Homogenization Theory held in Trieste, Italy, from January 15 to 26, 1990. The workshop was organized by the International Centre for Theo retical Physics (ICTP); part of the activity was co-sponsored by the Interna tional School for Advanced Studies (SISSA). The workshop covered a broad range of topics in the mathematical the ory of composite materials and homogenization. Among the specific areas of focus were homogenization of periodic and nonperiodic structures, porous me dia, asymptotic analysis for linear and nonlinear problems, optimal bounds for effective moduli, waves in composite materials, optimal design and relaxation, random media. The workshop was actively attended by more than 100 participants from 23 countries. In the afternoon sessions 35 seminars were delivered by the participants. This volume contains research articles corresponding to 14 of the 20 invited talks which were presented. Its content will be of interest both to mathematicians working in the field and to applied mathematicians and engineers interested in modelling the behaviour of composite and random media We are pleased to express here our thanks to the ICTP for having made this workshop possible, to Ms. A. Bergamo for her continuous help during the workshop, and to Ms. C. Parma for her collaboration in editing the proceedings. Gianni Dal Maso Gian Fausto Dell'Antonio SIS SA, Trieste Universita "La Sapienza", Roma v Contents Preface ... v List of Speakers ... ix Contributors ... ... ... ... . xiii ... ... ...
Game Theory And Partial Differential Equations
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Author : Pablo Blanc
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-22
Game Theory And Partial Differential Equations written by Pablo Blanc and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.