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.
Table of Contents
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
"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