Gaussian Hilbert Spaces

Zusammenfassung 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. Inhaltsverzeichnis 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.

Product details

• Authors: Svante Janson
• Assisted by: Bela Bollobas (Editor), W. Fulton (Editor)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 12.06.1997
• EAN: 9780521561280
• ISBN: 978-0-521-56128-0
• No. of pages: 352
• Series: Cambridge Tracts in Mathematic
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics