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Theory of Probability and Mathematical Statistics

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On some properties of asymptotic quasi-inverse functions


Authors: V. V. Buldygin, O. I. Klesov and J. G. Steinebach
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 15-30
MSC (2000): Primary 26A12; Secondary 26A48
DOI: https://doi.org/10.1090/S0094-9000-09-00744-3
Published electronically: January 14, 2009
MathSciNet review: 2432769
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Abstract: A characterization of normalizing functions connected with the limiting behavior of ratios of asymptotic quasi-inverse functions is discussed. For nondecreasing functions, conditions are obtained that are necessary and sufficient for their asymptotic quasi-inverse functions to belong to the class of (so-called) $ O$-regularly varying functions or to some of its subclasses.


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Additional Information

V. V. Buldygin
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue 37, Kyiv 03056, Ukraine
Email: valbuld@comsys.ntu-kpi.kiev.ua

O. I. Klesov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue 37, Kyiv 03056, Ukraine
Email: klesov@math.uni-paderborn.de

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

DOI: https://doi.org/10.1090/S0094-9000-09-00744-3
Received by editor(s): December 25, 2006
Published electronically: January 14, 2009
Additional Notes: This work was partially supported by Deutsche Forschungsgemeinschaft under DFG grants 436 UKR 113/41/0-3 and 436 UKR 113/68/0-1
Article copyright: © Copyright 2009 American Mathematical Society