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Long-Range Dependence and Self-Similarity
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Table of Contents

List of abbreviations; Notation; Preface; 1. A brief overview of times series and stochastic processes; 2. Basics of long-range dependence and self-similarity; 3. Physical models for long-range dependence and self-similarity; 4. Hermite processes; 5. Non-central and central limit theorems; 6. Fractional calculus and integration of deterministic functions with respect to FBM; 7. Stochastic integration with respect to fractional Brownian motion; 8. Series representations of fractional Brownian motion; 9. Multidimensional models; 10. Maximum likelihood estimation methods; Appendix A. Auxiliary notions and results; Appendix B. Integrals with respect to random measures; Appendix C. Basics of Malliavin calculus; Appendix D. Other notes and topics; Bibliography; Index.

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A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.

About the Author

Vladas Pipiras is Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. His research focuses on stochastic processes exhibiting long-range dependence, self-similarity, and other scaling phenomena, as well as on stable, extreme-value and other distributions possessing heavy tails. His other current interests include high-dimensional time series, sampling issues for 'big data', and stochastic dynamical systems, with applications in econometrics, neuroscience, engineering, computer science, and other areas. He has written over fifty research papers and is coauthor of A Basic Course in Measure and Probability: Theory for Applications (with Ross Leadbetter and Stamatis Cambanis, Cambridge, 2014) Murad S. Taqqu's research involves self-similar processes, their connection to time series with long-range dependence, the development of statistical tests, and the study of non-Gaussian processes whose marginal distributions have heavy tails. He has written more than 250 scientific papers and is coauthor of Stable Non-Gaussian Random Processes (with Gennady Samorodnitsky, 1994). Professor Taqqu is a Fellow of the Institute of Mathematical Statistics and has been elected Member of the International Statistical Institute. He has received a number of awards, including a John Simon Guggenheim Fellowship, the 1995 William J. Bennett Award, the 1996 Institute of Electrical and Electronics Engineers W. R. G. Baker Prize, the 2002 EURASIP Best Paper in Signal Processing Award, and the 2006 Association for Computing Machinery Special Interest Group on Data Communications (ACM SIGCOMM) Test of Time Award.

Reviews

'This is a marvelous book that brings together both classical background material and the latest research results on long-range dependence. The book is written so that it can be used as a main source by a graduate student, including all the essential proofs. I highly recommend this book.' Mark M. Meerschaert, Michigan State University
'This volume lays a rock-solid foundation for the subjects of long-range dependence and self-similarity. It also provides an up-to-date survey of more specialized topics at the center of this research area. The text is very readable and suitable for graduate courses, as it is self-contained and does not require more than an introductory course on stochastic calculus and time series. It is also written with the necessary level of mathematical detail to make it suitable for self-study. I particularly enjoyed the very nice introduction to fractional Brownian motion, its different representations, its stochastic calculus, and the connection to fractional calculus. I strongly recommend this book, which is a welcome addition to the literature and useful for a large audience.' Eric Moulines, Centre de Mathematiques Appliquees, Ecole Polytechnique, Paris
'This book provides a modern, rigorous introduction to long-range dependence and self-similarity. The authors write with wonderful clarity, covering fundamental as well as selected specialized topics. The book can be highly recommended to anybody interested in mathematical foundations of long memory and self-similar processes.' Jan Beran, University of Konstanz, Germany
'This is the most readable and lucid account I have seen on long-range dependence and self-similarity. Pipiras and Taqqu present a time-series-centric view of this subject that should appeal to both practitioners and researchers in stochastic processes and statistics. I was especially enamored by the insightful comments on the history of the subject that conclude each chapter. This alone is worth the price of the book!' Richard Davis, Columbia University, New York
Advance praise: 'This is a marvelous book that brings together both classical background material and the latest research results on long-range dependence. The book is written so that it can be used as a main source by a graduate student, including all the essential proofs. I highly recommend this book.' Mark M. Meerschaert, Michigan State University
Advance praise: 'This volume lays a rock-solid foundation for the subjects of long-range dependence and self-similarity. It also provides an up-to-date survey of more specialized topics at the center of this research area. The text is very readable and suitable for graduate courses, as it is self-contained and does not require more than an introductory course on stochastic calculus and time series. It is also written with the necessary level of mathematical detail to make it suitable for self-study. I particularly enjoyed the very nice introduction to fractional Brownian motion, its different representations, its stochastic calculus, and the connection to fractional calculus. I strongly recommend this book, which is a welcome addition to the literature and useful for a large audience.' Eric Moulines, Centre de Mathematiques Appliquees, Ecole Polytechnique, Paris
Advance praise: 'This book provides a modern, rigorous introduction to long-range dependence and self-similarity. The authors write with wonderful clarity, covering fundamental as well as selected specialized topics. The book can be highly recommended to anybody interested in mathematical foundations of long memory and self-similar processes.' Jan Beran, University of Konstanz, Germany
Advance praise: 'This is the most readable and lucid account I have seen on long-range dependence and self-similarity. Pipiras and Taqqu present a time-series-centric view of this subject that should appeal to both practitioners and researchers in stochastic processes and statistics. I was especially enamored by the insightful comments on the history of the subject that conclude each chapter. This alone is worth the price of the book!' Richard Davis, Columbia University, New York

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