Asymptotic Theory of Weakly Dependent Random Processes. 1st ed. 2017

種類:

電子ブック

責任表示:

by Emmanuel Rio

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017

著者名:

• Rio, Emmanuel.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 80

ISBN:

9783662543238 [3662543230]    

注記:

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

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