Druck auf Anfrage Neuware - Printed after ordering - 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 L�vy 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 L�vy processes.The first part of the book deals with the classical Brownian motion case. The second extends it to the L�vy 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 ofprobability 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.

N� de ref. del art�culo 9780387894874

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Detalles bibliogr�ficos

T�tulo

Stochastic Partial Differential Equations : A Modeling, White Noise Functional Approach

Editor

Springer New York

Fecha de publicaci�n

2009

Idioma

Ingl�s

ISBN 10

038789487X

ISBN 13

9780387894874

Encuadernaci�n

Taschenbuch

Edici�n

2� Edici�n

Estado

Neu

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Sinopsis

In this second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time L�vy process noise. Applications of the theory are emphasized throughout and useful exercises are at the end of each chapter.

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Helge Holden is a professor of mathematics at the Norwegian University of Science and Technology and an adjunt professor at the Center of Mathematics for Applications, part of the University of Oslo. He has done extensive research in stochastic analysis, in particular in its application to flow in porous media.

Bernt �ksendal is a professor at the Center of Mathematics for Applications at the University of Oslo. He is a winner of the Nansen Prize for research in stochastic analysis and its applications.

Jan Ub�e is a professor in the Department of Finance and Management Sciences at the Norwegian School of Economics and Business Administration. He has written many papers about this subject.

Tusheng Zhang is a professor of probability at the University of Manchester. His current area of research is stochastic differential and partial differential equations, and he recently published a monograph on fractional Brownian fields with Bernt �ksendal and others.

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