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130626  eng 
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a 9780387894881

100 
1 

a Holden, Helge

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0 
0 
a Stochastic Partial Differential Equations
h Elektronische Ressource
b A Modeling, White Noise Functional Approach
c by Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

250 


a 2nd ed. 2010

260 


a New York, NY
b Springer New York
c 2010, 2010

300 


a XV, 305 p. 17 illus
b online resource

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0 

a 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 Lévy white noise  Appendix A. The BochnerMinlos 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 Lévy processes References  List of frequently used notation and symbols  Index

653 


a Mathematical analysis

653 


a Probability Theory

653 


a Analysis

653 


a Mathematical Modeling and Industrial Mathematics

653 


a Differential Equations

653 


a Differential equations

653 


a Probabilities

653 


a Mathematical models

700 
1 

a Øksendal, Bernt
e [author]

700 
1 

a Ubøe, Jan
e [author]

700 
1 

a Zhang, Tusheng
e [author]

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0 
7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

490 
0 

a Universitext

028 
5 
0 
a 10.1007/9780387894881

856 
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0 
u https://doi.org/10.1007/9780387894881?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515

520 


a 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.

520 


a The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by spacetime Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by spacetime 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.

520 


a 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...
