Gaussian Hilbert Spaces

by Svante Janson

Overview

This book treats the very special and fundamental mathematical properties of a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, statistics and theoretical physics. The book concentrates on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.

Product Details

ISBN-13:	9780521561280
Publisher:	Cambridge University Press
Publication date:	06/12/1997
Series:	Cambridge Tracts in Mathematics , #129
Pages:	352
Product dimensions:	6.18(w) x 9.29(h) x 0.94(d)

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.

Editorial Reviews

"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

From the Publisher