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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 37-52
MSC (2000): Primary 26A12; Secondary 60F15
Published electronically: December 28, 2005
MathSciNet review: 2144319
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Abstract | References | Similar Articles | Additional Information

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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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

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00646-0
PII: S 0094-9000(05)00646-0
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