Some properties of asymptotic quasi-inverse functions and their applications I
Authors:
V. V. Buldygin, O. I. Klesov and J. G. Steinebach
Translated by:
The authors
Journal:
Theor. Probability and Math. Statist. 70 (2005), 11-28
MSC (2000):
Primary 26A12; Secondary 60F15
DOI:
https://doi.org/10.1090/S0094-9000-05-00627-7
Published electronically:
August 5, 2005
MathSciNet review:
2109819
Full-text PDF Free Access
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Abstract: We introduce the notions of asymptotic quasi-inverse functions and asymptotic inverse functions as weaker versions of (quasi-)inverse functions, and study their main properties. Asymptotic quasi-inverse functions exist in the class of so-called pseudo-regularly varying (PRV) functions, i.e. functions preserving the asymptotic equivalence of functions and sequences. On the other hand, asymptotic inverse functions exist in the class of so-called POV functions, i.e., functions with positive order of variation. In this paper, we obtain some new results about PRV and POV functions. Some further properties of asymptotic (quasi-)inverse functions as well as some applications will be discussed in Part II of this paper to appear in no. 71 of this journal.
References
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Additional Information
V. V. Buldygin
Affiliation:
Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), Peremogy 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 37, Kyiv 03056, Ukraine
Email:
oleg@tbimc.freenet.kiev.ua
J. G. Steinebach
Affiliation:
Universität zu Köln, Mathematisches Institut, Weyertal 86–90, D–50931 Köln, Germany
Email:
jost@math.uni-koeln.de
Received by editor(s):
September 14, 2003
Published electronically:
August 5, 2005
Additional Notes:
This work was partially supported by Deutsche Forschungsgemeinschaft under DFG grants 436 UKR 113/41/0-2 and 436 UKR 113/68/0-1.
Article copyright:
© Copyright 2005
American Mathematical Society
