Publications de l'Institut Mathématique, Nouvelle SérieVol. 80(94), pp. 59–96 (2006)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 80(94), pp. 59–96 (2006) |
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ON SOME EXTENSIONS OF KARAMATA'S THEORY AND THEIR APPLICATIONSV. V. Buldygin, O. I. Klesov, and J. G. SteinebachDepartment 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, GermanyAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
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