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Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction /
"Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard an...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
©2012.
|
| Colección: | Cambridge tracts in mathematics ;
191. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Preface
- 2. Martingales
- 3. Fourier and Laplace transformations
- 4. Abstract Wiener-Fréchet spaces
- 5. Two concepts of no-anticipation in time
- 6. Malliavin calculus on the space of real sequences
- 7. Introduction to poly-saturated models of mathematics
- 8. Extension of the real numbers
- 9. Topology
- 10. Measure and integration on Loeb spaces
- 11. From finite- to infinite-dimensional Brownian motion
- 12. The Itô integral for infinite-dimensional Brownian motion
- 13. Multiple integrals
- 14. Infinite-dimensional Ornstein-Uhlenbeck processes
- 15. Lindstrøm's construction of standard Lévy processes from discrete ones
- 16. Stochastic integration for Lévy processes
- 17. Chaos decomposition (for infinite-dimensional Brownian motion)
- 18. The Malliavin derivative
- 19. The Skorohod integral
- 20. The interplay between derivative and integral
- 21. Skorohod integral processes
- 22. Girsanov transformations
- 23. Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations)
- 24. Poly-saturated models
- 25. The existence of poly-saturated models
- References
- Index.