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Asymptotic theory of weakly dependent random processes

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Asymptotic theory of weakly dependent random processes/ by Emmanuel Rio.
Author:	Rio, Emmanuel.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2017.,
Description:	xviii, 204 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Statistical hypothesis testing - Asymptotic theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-662-54323-8
ISBN:	9783662543238

Asymptotic theory of weakly dependent random processes
Rio, Emmanuel.

Asymptotic theory of weakly dependent random processes[electronic resource] /by Emmanuel Rio. - Berlin, Heidelberg :Springer Berlin Heidelberg :2017. - xviii, 204 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.802199-3130 ;. - Probability theory and stochastic modelling ;v.72..

Introduction -- Variance of partial sums -- Algebraic moments. Elementary exponential inequalities -- Maximal inequalities and strong laws -- Central limit theorems -- Coupling and mixing -- Fuk-Nagaev inequalities, applications -- Empirical distribution functions -- Empirical processes indexed by classes of functions -- Irreducible Markov chains -- Appendices -- References -- Index.

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 "Theorie asymptotique des processus aleatoires faiblement dependants" (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.

ISBN: 9783662543238

Standard No.: 10.1007/978-3-662-54323-8doiSubjects--Topical Terms:

1141731
Statistical hypothesis testing
--Asymptotic theory.

LC Class. No.: QA277

Dewey Class. No.: 519.62

Asymptotic theory of weakly dependent random processes
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505 0 $a Introduction -- Variance of partial sums -- Algebraic moments. Elementary exponential inequalities -- Maximal inequalities and strong laws -- Central limit theorems -- Coupling and mixing -- Fuk-Nagaev inequalities, applications -- Empirical distribution functions -- Empirical processes indexed by classes of functions -- Irreducible Markov chains -- Appendices -- References -- Index.
520 $a 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 "Theorie asymptotique des processus aleatoires faiblement dependants" (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.
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650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
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