Convergence of Dependent Random Variables: Central Limit Theorems, Berry-Esseen Bounds, Martingale-like Sequences, C-sequences, Strong Laws - Couverture souple

Tuyen, Dao Quang

 
9783843355629: Convergence of Dependent Random Variables: Central Limit Theorems, Berry-Esseen Bounds, Martingale-like Sequences, C-sequences, Strong Laws
Couverture souple
ISBN 10 : 3843355622 ISBN 13 : 9783843355629
Editeur : LAP LAMBERT Academic Publishing, 2010

Synopsis

Central Limit Theorems, Rates of Convergence are derived for dependent random variables, with relaxed conditions on the dependence. Most of known mixing conditions like strong (alpha-) mixing, absolute regular (beta-mixing),... will satisfy them. This new notion of measure of dependence is developed naturally from the classical Characteristic Function Method, less intuitive but may be more suitable in applications than mixing ones. As it is born from the well-known tool for independent r.v.s's Limit Theorems. Theorems and examples given here prove this notion. Otherwise, it may reach the limit in process of defining measure of the dependence, as argued in this book. On the other aspect, almost sure convergence of adapted sequence, especially of Martingale-like one, is discussed. C-sequence is created, showed not comparative with Amart, Martingale-in-the-limit, by examples. It also is a natural extension of Martingale, derived by seeking condition ensuring a.s. convergence. Also, a phi-mixing Strong Law and some examples of Linear Process are given.

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Présentation de l'éditeur

Central Limit Theorems, Rates of Convergence are derived for dependent random variables, with relaxed conditions on the dependence. Most of known mixing conditions like strong (alpha-) mixing, absolute regular (beta-mixing),... will satisfy them. This new notion of measure of dependence is developed naturally from the classical Characteristic Function Method, less intuitive but may be more suitable in applications than mixing ones. As it is born from the well-known tool for independent r.v.s's Limit Theorems. Theorems and examples given here prove this notion. Otherwise, it may reach the limit in process of defining measure of the dependence, as argued in this book. On the other aspect, almost sure convergence of adapted sequence, especially of Martingale-like one, is discussed. C-sequence is created, showed not comparative with Amart, Martingale-in-the-limit, by examples. It also is a natural extension of Martingale, derived by seeking condition ensuring a.s. convergence. Also, a phi-mixing Strong Law and some examples of Linear Process are given.

Biographie de l'auteur

D. Q. Tuyen, Ph.D.: Graduated at Eötvös Loránd University in Budapest. Obtained Ph.D. at Karl-Weierstrass-Institute of Mathematics in Berlin. Researcher at Institute of Mathematics of Hanoi.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
3843355622
ISBN 13 
9783843355629
Reliure
Broché
Nombre de pages
124
Coordonnées du fabricant
non disponible
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