Stable non-Gaussian random processes
Subtitle: stochastic models with infinite variance
By: Gennady Samorodnitsky, Murad S. Taqqu.
Contributors: Taqqu, Murad S.
Series: Stochastic modeling
Publisher: Chapman & Hall
Published: 1994
Place of publication: New York
Language: eng
Number of pages: 632
Subjects: Gaussian processes.; Gaussian distribution.
Description: The familiar Gaussian models do not allow for large deviations and are thus often inadequate for modeling high variability. Non-Gaussian stable models do not possess such limitations. They all share a familiar feature which differentiates them from the Gaussian ones. Their marginal distributions possess heavy "probability tails," always with infinite variance and in some cases with infinite first moment.

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only a first-year graduate course in probability, it includes material which has appeared only recently in journals and unpublished materials.

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 includes a discussion of self-similar processes, ARMA, and fractional ARIMA time series with stable innovations.
Notes: Includes bibliographical references (p. [603]-619) and indexes.