Authors:
- Each chapter ends with a set of exercises
- Provides a detailed exposition of optimal asymptotics results for strongly mixing sequences
- English translation is an updated and revised edition
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 80)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular.
The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises.
The book is an updated and extended translation of the French edition entitled "Théorie asymptotique des processus aléatoires faiblement dépendants" (Springer, 2000). It will be useful for students and researchers in mathematical statistics, econometrics, probability theory and dynamical systems who are interested in weakly dependent processes.
Authors and Affiliations
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Laboratoire de Mathématiques, Université de Versailles, Versailles, France
Emmanuel Rio
About the author
Bibliographic Information
Book Title: Asymptotic Theory of Weakly Dependent Random Processes
Authors: Emmanuel Rio
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-662-54323-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany 2017
Hardcover ISBN: 978-3-662-54322-1Published: 02 May 2017
Softcover ISBN: 978-3-662-57191-0Published: 25 July 2018
eBook ISBN: 978-3-662-54323-8Published: 13 April 2017
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XVIII, 204
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Game Theory, Economics, Social and Behav. Sciences