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Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach (Probability and its Applications) - Hardcover
Synopsis
The main emphasis of this work is on stochastic partial differential equations. First the stochastic Poisson equation and the stochastic transport equation are discussed; then the authors go on to deal with the Schrodinger equation, the heat equation, the nonlinear Burgers' equation with a stochastic source, and the pressure equation. The white noise approach often allows for solutions given by explicit formulas in terms of expectations of certain auxiliary processes. The noise in the above examples are all of a Gaussian white noise type. In the end, the authors also show how to adapt the analysis to SPDEs involving noise of Poissonian type.
"synopsis" may belong to another edition of this title.
Review
"The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book... It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." ―Mathematical Reviews
"...a comprehensive introduction to stochastic partial differential equations." ―Zentralblatt MATH
"This book will be invaluable to anyone interested in doing research in white noise theory or in applying this theory to solving real-world problems." ―Computing Reviews
From the Back Cover
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by space-time Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by space-time Lévy process noise, and introduce new applications of the field.
Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Lévy processes.
The first part of the book deals with the classical Brownian motion case. The second extends it to the Lévy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermite transform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance.
Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.
From the reviews of the first edition:
"The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book... It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." ―Mathematical Reviews
"...a comprehensive introduction to stochastic partial differential equations." ―Zentralblatt MATH
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- PublisherBirkhauser Verlag AG
- Publication date1996
- ISBN 10 3764339284
- ISBN 13 9783764339289
- BindingHardcover
- LanguageEnglish
- Number of pages231
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Stochastic partial differential equations : a modeling, white noise functional approach
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Boston [u.a.] : Birkhäuser, 1996
ISBN 10: 3764339284
ISBN 13: 9783764339289
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Stochastic Partial Differential Equations
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. KlappentextThis 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 co. Seller Inventory # 5279048
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Stochastic Partial Differential Equations
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ISBN 10: 3764339284
ISBN 13: 9783764339289
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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 248 pp. Englisch. Seller Inventory # 9783764339289
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Stochastic Partial Differential Equations : A Modeling, White Noise Functional Approach
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783764339289
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Stochastic partial differential equations: A modeling, white noise functional approach (Probability and its applications)
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