Overview
- 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
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Stochastic Processes and Long Range Dependence
Authors: Gennady Samorodnitsky
Series Title: Springer Series in Operations Research and Financial Engineering
DOI: https://doi.org/10.1007/978-3-319-45575-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-45574-7Published: 16 November 2016
Softcover ISBN: 978-3-319-83321-7Published: 28 June 2018
eBook ISBN: 978-3-319-45575-4Published: 09 November 2016
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 1
Number of Pages: XI, 415
Number of Illustrations: 5 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Measure and Integration, Dynamical Systems and Ergodic Theory