Asymptotic Theory of Weakly Dependent Random Processes

  • Emmanuel Rio

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 80)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Emmanuel Rio
    Pages 1-32
  3. Emmanuel Rio
    Pages 51-63
  4. Emmanuel Rio
    Pages 65-87
  5. Emmanuel Rio
    Pages 89-100
  6. Emmanuel Rio
    Pages 101-111
  7. Emmanuel Rio
    Pages 113-124
  8. Emmanuel Rio
    Pages 149-169
  9. Back Matter
    Pages 171-204

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.


60-01, 60F05, 60F15, 60F17, 60E15, 60G10, 60J10, 62G07 strongly mixing sequences absolutely regular sequences moment inequalities deviation inequalities strong laws of large numbers central limit theorem coupling empirical processes Markov chains covariance inequalities

Authors and affiliations

  • Emmanuel Rio
    • 1
  1. 1.Laboratoire de MathématiquesUniversité de VersaillesVersaillesFrance

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