EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 59–96 (2006)

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V. V. Buldygin, O. I. Klesov, and J. G. Steinebach

Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), pr. Peremogy, 37 3056 Kyiv Ukraine; and Mathematisches Institut, Universität zu Köln, Weyertal 86–90, D–50931 Köln, Germany

Abstract: This is a survey of the authors' results on the properties and applications of some subclasses of (so-called) $O$-regularly varying (ORV) functions. In particular, factorization and uniform convergence theorems for Avakumovic–Karamata functions with non-degenerate groups of regular points are presented together with the properties of various other extensions of regularly varying functions. A discussion of equivalent characterizations of such classes of functions is also included as well as that of their (asymptotic) inverse functions. Applications are given concerning the asymptotic behavior of solutions of certain stochastic differential equations.

Keywords: Karamata's theory; $O$-regular variation; representation theorem; asymptotic inverse; renewal theory; stochastic differential equation

Classification (MSC2000): 26-02; 60-02; 26A12; 60F15; 60H10; 60K05

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

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