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 analysis...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2012.
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| Series: | Cambridge tracts in mathematics ;
191. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Martingales
- Fourier and Laplace transformations
- Abstract Wiener-Fréchet spaces
- Two concepts of no-anticipation in time
- Malliavin calculus on the space of real sequences
- Introduction to poly-saturated models of mathematics
- Extension of the real numbers
- Topology
- Measure and integration on Loeb spaces
- From finite- to infinite-dimensional Brownian motion
- The Itô integral for infinite-dimensional Brownian motion
- Multiple integrals
- Infinite-dimensional Ornstein-Uhlenbeck processes
- Lindstrøm's construction of standard Lévy processes from discrete ones
- Stochastic integration for Lévy processes
- Chaos decomposition (for infinite-dimensional Brownian motion)
- The Malliavin derivative
- The Skorohod integral
- The interplay between derivative and integral
- Skorohod integral processes
- Girsanov transformations
- 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)
- Poly-saturated models
- The existence of poly-saturated models.
