Stable Convergence and Stable Limit Theorems

Harald Luschgy

ISBN 10: 3319183281 / ISBN 13: 9783319183282

Verlag: Springer International Publishing, Springer Nature Switzerland Jun 2015, 2015

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 240 pp. Englisch.

Bestandsnummer des Verkäufers 9783319183282

Bibliografische Details

• Titel: Stable Convergence and Stable Limit Theorems
• Verlag: Springer International Publishing, Springer Nature Switzerland Jun 2015
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 3319183281
• ISBN-13: 9783319183282
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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 die Autorin bzw. 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.