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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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) -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