Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Stochastic Modeling Series) - Hardcover

Gennady Samorodnitsky

Hardcover

ISBN 10: 0412051710 ISBN 13: 9780412051715

Publisher: Routledge, 1994

Synopsis

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.

About this title

About the Author

Samoradnitsky, Gennady

From the Back Cover

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a first-year graduate course in probability, it includes material which has appeared only recently in journals and unpublished materials.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

Edition details

• Publisher: Routledge
• Publication date: 1994
• Language: English
• ISBN 10: 0412051710
• ISBN 13: 9780412051715
• Binding: Hardcover
• Edition number: 1
• Number of pages: 654