Gaussian Hilbert Spaces
Gaussian Hilbert Spaces
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This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and theoretical physics. The emphasis throughout this book is on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.
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"The book is written in a clear...style and can also be used as the backbone of a graduate course on stochastic analysis with a view towards the applications in physics..." Monatshefte fur Mathematik
Product details
July 1997Hardback
9780521561280
352 pages
236 × 157 × 24 mm
0.638kg
Available
Table of Contents
- 1. Gaussian Hilbert spaces
- 2. Wiener chaos
- 3. Wick products
- 4. Tensor products and Fock spaces
- 5. Hypercontractivity
- 6. Distributions of variables with finite chaos expansions
- 7. Stochastic integration
- 8. Gaussian stochastic processes
- 9. Conditioning
- 10. Limit theorems for generalized U-statistics
- 11. Applications to operator theory
- 12. Some operators from quantum physics
- 13. The Cameron-Martin shift
- 14. Malliavin calculus
- 15. Transforms
- Appendices.
