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**
Gennady Samorodnitsky and Murad S. Taqqu **

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*STABLE NON-GAUSSIAN RANDOM PROCESSES:*

* STOCHASTIC MODELS WITH INFINITE VARIANCE*

Chapman and Hall, New York,
1994

ISBN 0-412-05171-0,
656 pages,

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** **## ABSTRACT

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

*Murad Taqqu *

Sun Mar 31 21:56:53 EST 1996