Stable Non-Gaussian Random Processes

This book presents similarity between Gaussian and non-Gaussian stable multivariate distributions and introduces the one-dimensional stable random variables. It discusses the most basic sample path properties of stable processes, namely sample boundedness and continuity.

"There has been a pressing need for a book on this subject...The authors have succeeded in filling the gap...I am very glad a standard reference about stable processes now exists."- Bulletin of the London Mathematical Society

Autorentext
Samoradnitsky, Gennady

Klappentext

This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability.

Inhalt

1. Stable random variables on the real line 2. Multivariate stable distributions 3. Stable random processes and stochastic integrals 4. Dependence Structures of Multivariate Stable Distributions 5. Non-linear regression 6. Complex stable stochastic integrals and harmonizable processes 7. Self-similar processes 8. Chentsov random fields 9. Introduction to sample path properties 10. Boundedness, continuity and oscillations 11. Measurability, integrability and absolute continuity 12. Boundedness and continuity via metric entropy 13. Integral representation 14. Historical notes and extensions