Stable Non-Gaussian Random Processes

Stochastic Models with Infinite Variance

By: Gennady Samoradnitsky

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Hardcover | 1 June 1994 | Edition Number 1

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Hardcover
654 Pages

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Up to 18

Dimensions(cm)
22.9 x 15.2 x 4.5

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a first-year graduate course in probability, it includes material which has appeared only recently in journals and unpublished materials.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

Industry Reviews

"There has been a pressing need for a book on this subject...The authors have succeeded in filling the gap...I am very glad a standard reference about stable processes now exists." - Bulletin of the London Mathematical Society

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