Produktbild: Stochastic Partial Differential Equations

Stochastic Partial Differential Equations A Modeling, White Noise Functional Approach

Fr. 191.00

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

16.06.2012

Abbildungen

XII, 231 p.

Verlag

Birkhäuser Boston

Seitenzahl

231

Maße (L/B/H)

23.5/15.5/1.4 cm

Gewicht

382 g

Auflage

Softcover reprint of the original 1st ed. 1996

Sprache

Englisch

ISBN

978-1-4684-9217-0

Beschreibung

Rezension

"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

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

16.06.2012

Abbildungen

XII, 231 p.

Verlag

Birkhäuser Boston

Seitenzahl

231

Maße (L/B/H)

23.5/15.5/1.4 cm

Gewicht

382 g

Auflage

Softcover reprint of the original 1st ed. 1996

Sprache

Englisch

ISBN

978-1-4684-9217-0

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: Stochastic Partial Differential Equations
  • 1. Introduction.- 1.1. Modeling by stochastic differential equations.- 2. Framework.- 2.1. White noise.- 2.2. The Wiener-Itô chaos expansion.- 2.3. Stochastic test functions and stochastic distributions.- 2.4. The Wick product.- 2.5. Wick multiplication and Itô/Skorohod integration.- 2.6. The Hermite transform.- 2.7. The S)p,rN spaces and the S-transform.- 2.8. The topology of (S)-1N.- 2.9. The F-transform and the Wick product on L1 (?).- 2.10. The Wick product and translation.- 2.11. Positivity.- 3. Applications to stochastic ordinary differential equations.- 3.1. Linear equations.- 3.2. A model for population growth in a crowded stochastic environment.- 3.3. A general existence and uniqueness theorem.- 3.4. The stochastic Volterra equation.- 3.5. Wick products versus ordinary products: A comparison experiment Variance properties.- 3.6. Solution and Wick approximation of quasilinear SDE.- 4. Stochastic partial differential equations.- 4.1. General remarks.- 4.2. The stochastic Poisson equation.- 4.3. The stochastic transport equation.- 4.4. The stochastic Schrödinger equation.- 4.5. The viscous Burgers’ equation with a stochastic source.- 4.6. The stochastic pressure equation.- 4.7. The heat equation in a stochastic, anisotropic medium.- 4.8. A class of quasilinear parabolic SPDEs.- 4.9. SPDEs driven by Poissonian noise.- Appendix A. The Bochner-Minlos theorem.- Appendix B. A brief review of Itô calculus.- The Itô formula.- Stochastic differential equations.- The Girsanov theorem.- Appendix C. Properties of Hermite polynomials.- Appendix D. Independence of bases in Wick products.- References.- List of frequently used notation and symbols.