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a first-year graduate course in probability, it includes material which has appeared only recently in journals and unpublished materials.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

There has been extensive research in the past twenty years devoted to a better understanding of the stable and other closely related infinitely divisible models. The late Professor Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these fields from the early seventies until his untimely death in April 1995. This commemorative volume honoring Stamatis Cambanis consists of a collection of research articles devoted to review the state of the art in rapidly developing research areas in Stochastic Processes and to explore new directions of research. The volume is a tribute to the life and work of Stamatis by his students, friends, and colleagues whose personal and professional lives he deeply touched through his generous insights and dedication to his profession.