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Field name	Details
Dewey Class	519.2
Title	Stochastic Partial Differential Equations ([EBook]) : A Modeling, White Noise Functional Approach / by Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang.
Author	Holden, Helge. , 1956-
Added Personal Name	Øksendal, Bernt
	Ubøe, Jan
	Zhang, Tusheng
Other name(s)	SpringerLink (Online service)
Edition statement	Second edition
Publication	New York, NY : Springer , 2010.
Physical Details	: online resource.
Series	Universitext
ISBN	9780387894881
Summary Note	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 LÃ©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 LÃ©vy processes. The first part of the book deals with the classical Brownian motion case. The second extends it to the LÃ©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 bookâ¦ It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." âMathematical Reviews "...a comprehensive introduction to stochastic partial differential equations." âZentralblatt MATH:
Contents note	Preface to the Second Edition -- Preface to the First Edition -- Introduction -- Framework -- Applications to stochastic ordinary differential equations -- Stochastic partial differential equations driven by Brownian white noise -- Stochastic partial differential equations driven by LÃ©vy white noise -- Appendix A. The Bochner-Minlos theorem -- Appendix B. Stochastic calculus based on Brownian motion -- Appendix C. Properties of Hermite polynomials -- Appendix D. Independence of bases in Wick products -- Appendix E. Stochastic calculus based on LÃ©vy processes- References -- List of frequently used notation and symbols -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-89488-1
Links to Related Works	Subject References: Differential equation . Differential equations, Partial . Distribution (Probability theory) . Mathematical Modeling and Industrial Mathematics . Mathematics . Ordinary differential equations . Partial differential equations . Probability theory and stochastic processes . Authors: author . Holden, Helge. 1956- . Øksendal, Bernt . Ubøe, Jan . Zhang, Tusheng . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 519.2 .

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

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