Gaussian Hilbert Spaces

This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.

Svante Janson (Author)

9780521561280, Cambridge University Press

Hardback, published 12 June 1997

352 pages
23.6 x 15.7 x 2.4 cm, 0.638 kg

' … a well-written study …' European Mathematical Society

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]