ABSTRACT

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. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.

chapter 1|54 pages

Stable random variables on the real line

chapter 2|56 pages

Multivariate stable distributions

chapter 5|48 pages

Non-linear regression

chapter 7|82 pages

Self-similar processes

chapter 8|28 pages

Chentsov random fields

chapter 9|26 pages

Introduction to sample path properties

chapter 10|52 pages

Boundedness, continuity and oscillations

chapter 13|12 pages

Integral representation

chapter 14|25 pages

Historical notes and extensions