Some properties of asymptotic quasi-inverse functions and their applications. II
Authors:
V. V. Buldygin, O. I. Klesov and J. G. Steinebach
Translated by:
The authors
Journal:
Theor. Probability and Math. Statist. 71 (2005), 37-52
MSC (2000):
Primary 26A12; Secondary 60F15
DOI:
https://doi.org/10.1090/S0094-9000-05-00646-0
Published electronically:
December 28, 2005
MathSciNet review:
2144319
Full-text PDF Free Access
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Abstract: We continue to study properties of functions which are asymptotic (quasi-)inverse for PRV and POV functions. The equivalence of all quasi-inverses for POV functions is proved. Under appropriate conditions, we derive the limiting behaviour of the ratio of asymptotic quasi-inverse functions from the corresponding asymptotics of their original versions. Several applications of these general results to the asymptotic stability of a Cauchy problem, to the asymptotics of the solution of a stochastic differential equation, and to the limiting behavior of generalized renewal processes are also presented.
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References
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Additional Information
V. V. Buldygin
Affiliation:
Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), Pr. 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), Pr. 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):
February 27, 2004
Published electronically:
December 28, 2005
Additional Notes:
This work has partially been 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