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Stochastic partial differential equations : a modeling, white noise functional approach /

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Holden, H. (Helge), 1956-
Format: eBook
Language:English
Published: Boston : Birkhauser Boston, 1996.
Series:Probability and its applications.
Subjects:
Stochastic partial differential equations.
Équations aux dérivées partielles stochastiques.
Stochastische differentiaalvergelijkingen.
Partiële differentiaalvergelijkingen.
Equations aux dérivés partielles stochastiques.
Stochastische partielle Differentialgleichung.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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 Schrdinger 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.