Stochastic Partial Differential Equations - Bernt Oksendal

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Biographie:
Helge Holden is?professor of mathematics at the Norwegian University of Science and Technology and an adjunct professor at the Center of Mathematics for Applications, part of the University of Oslo.? He has done extensive research in stochastic analysis, in particular in its application to flow in porous media. Nils Henrik Risebro is professor of mathematics at the University of Oslo. His?research interests are mainly nonlinear partial differential equations and numerical methods for these. He has?also worked on conservation laws with discontinuous coefficients in a variety of applications....

Sommaire:
1. Introduction.- 1.1. Modeling by stochastic differential equations.- 2. Framework.- 2.1. White noise.- 2.2. The Wiener-It? chaos expansion.- 2.3. Stochastic test functions and stochastic distributions.- 2.4. The Wick product.- 2.5. Wick multiplication and It?/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 Schr?dinger 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 It? calculus.- The It? 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.