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"...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
--This text refers to the Hardcover edition.
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
- Series: Universitext
- Paperback: 305 pages
- Publisher: Springer; 2nd ed. 2010 edition (December 4, 2009)
- Language: English
- ISBN-10: 038789487X
- ISBN-13: 978-0387894874
- Product Dimensions: 6 x 0.7 x 9 inches
- Shipping Weight: 1 pounds (View shipping rates and policies)
- Average Customer Review: 4.0 out of 5 stars See all reviews(3 customer reviews)
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.
This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.
- Series: Universitext
- Paperback: 379 pages
- Publisher: Springer; 6th edition (March 4, 2014)
- Language: English
- ISBN-10: 3540047581
- ISBN-13: 978-3540047582
- Product Dimensions: 6.1 x 0.9 x 9.2 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 4.0 out of 5 stars See all reviews(23 customer reviews)
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