Stochastic Processes and Long Range Dependence

  • Gennady Samorodnitsky

Table of contents

  1. Front Matter
    Pages i-xi
  2. Gennady Samorodnitsky
    Pages 1-26
  3. Gennady Samorodnitsky
    Pages 73-132
  4. Gennady Samorodnitsky
    Pages 133-173
  5. Gennady Samorodnitsky
    Pages 175-191
  6. Gennady Samorodnitsky
    Pages 193-228
  7. Gennady Samorodnitsky
    Pages 247-283
  8. Gennady Samorodnitsky
    Pages 285-361
  9. Gennady Samorodnitsky
    Pages 363-404
  10. Back Matter
    Pages 405-415

About this book

Introduction

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.

Keywords

Stochastic Processes Ergodic Theory Long Range Dependence Heavy Tails Second-order Theory

Authors and affiliations

  • Gennady Samorodnitsky
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-45575-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-45574-7
  • Online ISBN 978-3-319-45575-4
  • Series Print ISSN 1431-8598
  • Series Online ISSN 2197-1773
  • About this book
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