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Some properties of asymptotic quasi-inverse functions and their applications I
Author(s):
V.
V.
Buldygin;
O.
I.
Klesov;
J.
G.
Steinebach
Translated by:
The authors
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 70
(2004).
Journal:
Theor. Probability and Math. Statist.
No. 70
(2005),
11-28.
MSC (2000):
Primary 26A12;
Secondary 60F15
Posted:
August 5, 2005
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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.
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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
DOI:
10.1090/S0094-9000-05-00627-7
PII:
S 0094-9000(05)00627-7
Received by editor(s):
14/SEP/2003
Posted:
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.
Copyright of article:
Copyright
2005,
American Mathematical Society
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