Stable Convergence and Stable Limit Theorems

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Sprache: Englisch

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Beschreibung

The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics - such as the classical central limit theorem - which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.

Über den Autor

Erich Haeusler studied mathematics and physics at the University of Bochum from 1972 to 1978. He received his doctorate in mathematics in 1982 from the University of Munich. Since 1991 he has been Professor of Mathematics at the University of Giessen, where he teaches probability and mathematical statistics. Harald Luschgy studied mathematics, physics and mathematical logic at the Universities of Bonn and Münster. He received his doctorate in mathematics in 1976 from the University of Münster. He held visiting positions at the Universities of Hamburg, Bayreuth, Dortmund, Oldenburg, Passau and Wien and was a recipient of a Heisenberg grant from the DFG. Since 1995 he is Professor of Mathematics at the University of Trier where he teaches probability and mathematical statistics.

Zusammenfassung

First monograph entirely devoted to the subject of stable convergence

Presents a clear and sound introduction to the field

Includes examples of successful applications and exercise sets with solutions to illustrate the theoretical results

Inhaltsverzeichnis

Preface.- [...] Convergence of Markov Kernels.- 2.Stable Convergence.- 3.Applications.- 4.Stability of Limit Theorems.- 5.Stable Martingale Central Limit Theorems.- 6.Stable Functional Martingale Central Limit Theorems.- 7.A Stable Limit Theorem with Exponential Rate.- 8.Autoregression of Order One.- 9.Branching Processes.- A. Appendix.- B. Appendix.- Bibliography.

Details

Erscheinungsjahr:	2016
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	x 228 S.
ISBN-13:	9783319365190
ISBN-10:	3319365193
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Häusler, Erich Luschgy, Harald
Auflage:	Softcover reprint of the original 1st edition 2015
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 14 mm
Von/Mit:	Erich Häusler (u. a.)
Erscheinungsdatum:	15.10.2016
Gewicht:	0,371 kg