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An inequality for the Lévy distance between two distribution functions and its applications


Authors: K.-H. Indlekofer, O. I. Klesov and J. G. Steinebach
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 59-70
MSC (2010): Primary 60J05
DOI: https://doi.org/10.1090/S0094-9000-2010-00810-6
Published electronically: January 18, 2011
MathSciNet review: 2667310
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a nonuniform bound for the deviation between two distribution functions expressed in terms of the Lévy distance. Applications of this bound to the global version of the central limit theorem are given and complete convergence is shown.


References [Enhancements On Off] (What's this?)

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Additional Information

K.-H. Indlekofer
Affiliation: Fakultät für Elektrotechnik, Informatik und Mathematik, Institut für Mathematik, Universität Paderborn, Warburger Straße 100, Paderborn 33098, Germany
Email: k-heinz@uni-paderborn.de

O. I. Klesov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), Prospekt Peremogy 37, Kyiv 03056, Ukraine
Email: oleg@math.uni-paderborn.de

J. G. Steinebach
Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86–90, Köln D–50931, Germany
Email: jost@math.uni-koeln.de

DOI: https://doi.org/10.1090/S0094-9000-2010-00810-6
Keywords: Lévy distance, global version of the central limit theorem, complete convergence
Received by editor(s): September 11, 2009
Published electronically: January 18, 2011
Additional Notes: Supported by a DFG grant
Article copyright: © Copyright 2010 American Mathematical Society

American Mathematical Society