TY  - BOOK
AU  - Janson,Svante
TI  - Gaussian Hilbert spaces
T2  - Cambridge tracts in mathematics
SN  - 9780511526169 (ebook)
AV  - QA273.6 .J36 1997
U1  - 519.2 21
PY  - 1997///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Gaussian distribution
KW  - Hilbert space
KW  - Functions of complex variables
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Ch. 1. Gaussian spaces -- Ch. 2. Wiener chaos -- Ch. 3. Wick products -- Ch. 4. Tensor products and Fock space -- Ch. 5. Hypercontractivity -- Ch. 6. Variables with finite chaos decompositions -- Ch. 7. Stochastic integration -- Ch. 8. Gaussian stochastic processes -- Ch. 9. Conditioning -- Ch. 10. Pairs of Gaussian subspaces -- Ch. 11. Limit theorems for generalized U-statistics -- Ch. 12. Applications to operator theory -- Ch. 13. Some operators from quantum physics -- Ch. 14. The Cameron Martin shift -- Ch. 15. Malliavin calculus -- Ch. 16. Transforms -- App. A. The monotone class theorem -- App. B. Stochastic processes -- App. C. Banach-space-valued functions and random variables -- App. D. Polarization -- App. E. Tensor products -- App. F. Reproducing Hilbert Spaces -- App. G. Analytic functions in Banach spaces -- App. H. Hilbert-Schmidt operators and singular numbers
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511526169
ER  -