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Asymptotic Theory of Weakly Dependent Random Processes

Af: Emmanuel Rio Engelsk Paperback

Asymptotic Theory of Weakly Dependent Random Processes

Af: Emmanuel Rio Engelsk Paperback
Tjek vores konkurrenters priser
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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 204
ISBN-13: 9783662571910
Indbinding: Paperback
Udgave:
ISBN-10: 3662571919
Udg. Dato: 25 jul 2018
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Oplagsdato: 25 jul 2018
Forfatter(e): Emmanuel Rio
Forfatter(e) Emmanuel Rio


Kategori Differentialregning & ligninger


ISBN-13 9783662571910


Sprog Engelsk


Indbinding Paperback


Sider 204


Udgave


Længde 0mm


Bredde 155mm


Højde 235mm


Udg. Dato 25 jul 2018


Oplagsdato 25 jul 2018


Forlag Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

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