STABLE NON-GAUSSIAN RANDOM PROCESSES:
STOCHASTIC MODELS WITH INFINITE VARIANCE
Chapman and Hall, New York, 1994
ISBN 0-412-05171-0, 656 pages,
This book fills a gap that teachers and researchers in the field in probability have increasingly felt. Stable processes, which have attracted growing interest in recent years, are not the single subject of any monograph or comprehensive overview. This book serves both as an introduction to the subject and as a basic reference text.
The familiar Gaussian models are named after the German mathematician Carl Friedrich Gauss. Based on the usual "bell-shaped" probability curve, they do not allow for large deviations and are thus often inadequate for modelling high variability. In the last two or three decades however, data with heavy "probability tails" have been collected in fields as diverse as economics, telecommunications, hydrology and physics of condensed matter, suggesting the use of non-Gaussian stable processes as possible models. These models always have infinite variance and, in some cases, infinite mean as well.
The aim of this book is to make this exciting material easily accessible to graduate students and practitioners. Assuming only a first-year graduate course in probability, it includes material which has appeared only recently in journals and material not published anywhere.
Each chapter begins with a brief overview and concludes with a range of exercises at varying levels of difficulty. Proofs are spelled out in detail. The book also includes a discussion of self-similar processes ( "random fractals" ) and time series with long memory and stable innovations.
Gennady Samorodnitsky is Associate Professor in the School of Operations Research and Industrial Engineering at Cornell University. He is a Fellow of the Weizmann Institute.
Murad S. Taqqu is Professor in the Department of Mathematics at Boston University. He is Associate Editor of the journal Stochastic Processes and their Applications, a Fellow of the Institute of Mathematical Statistics and a Guggenheim Fellow.
Table of Contents (in Postcript) (in Acrobat format)
Can now be purchased from CRC Press