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Stochastic Partial Differential Equations

A Modeling, White Noise Functional Approach
BuchGebunden
Englisch
Birkhäuser Bostonerschienen am01.08.19961996
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S.mehr
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Produkt

KlappentextThis book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S.
Details
ISBN/GTIN978-0-8176-3928-0
ProduktartBuch
EinbandartGebunden
Erscheinungsjahr1996
Erscheinungsdatum01.08.1996
Auflage1996
ReiheProbability and Its Applications
SpracheEnglisch
MasseBreite 160 mm, Höhe 241 mm, Dicke 19 mm
Gewicht541 g
Artikel-Nr.11024295

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

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