This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author's own, less standard, point of view of long memory as a phase transition, and even includes some novel results.

Most of the material in the bookhas not previously been published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.

First book of its kind to offer a self-contained modern introduction to long-range dependence Written by a leading expert in the field; the product of many years of experience and insight Presents the reader with both the standard approach and the author's own, less standard, approach to long-range dependence Includes new results made by the author Includes supplementary material: sn.pub/extras

Autorentext

Gennady Samorodnitsky is a Professor in the School of Operations Research and Information Engineering at Cornell University. His interest lies both in probability theory and in its various applications.

Inhalt
Preface.- Stationary Processes.- Ergodic Theory of Stationary Processes.- Infinitely Divisible Processes.- Heavy Tails.- Hurst Phenomenon.- Second-order Theory.- Fractionally Integrated Processes.- Self-similar Processes.- Long Range Dependence as a Phase Transition.- Appendix.