Stochastic Processes and Long Range Dependence

ISBN-13: 9783319833217 / Angielski / Miękka / 2018 / 415 str.

Gennady Samorodnitsky

Recenzje

"This book is dedicated to the long-range dependence as a property of stationary stochastic processes. It is a very interesting, well-written and easy to read book and can be used as a source of information for students and researchers who want to learn about the long-range dependence property." (Miroslav M. Ristic, zbMATH 1376.60007, 2018)
"The author has achieved a remarkably balanced presentation: the book includes selective materials for a first class on stationary stochastic processes, explains important concepts and key developments for long-range dependence, illustrates with a large collection of important and representative examples, and points out at the end a very promising direction in the area. The monograph is an ideal textbook on stochastic processes with long-range dependence for a one- or two-semester course for graduate students." (Yizao Wany, Mathematical Reviews, October, 2017)

Spis treści

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.

O autorze

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.

Blurb

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 book has 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.