Gaussian Hilbert Spaces
Gaussian Hilbert Spaces
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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Reviews & endorsements
'This book could be an excellent text for students who would like to learn this subject, and it could also be helpful for researchers, taking into account the great care and completeness of its presentation.' Bulletin of the London Mathematics Society
' … a well-written study …' European Mathematical Society
Product details
June 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.
