Geodesic
On Some Extensions of Karamata's Theory and Their Applications
Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 59 .

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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 Avakumović--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.
DOI : 10.2298/PIM0694059B
Classification : 26-02 60-02 26A12 60F15 60H10 60K05
Keywords: Karamata's theory, $O$-regular variation, representation theorem, asymptotic inverse, renewal theory, stochastic differential equation 
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V. V. Buldygin; O. I. Klesov; J. G. Steinebach. On Some Extensions of Karamata's Theory and Their Applications. Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 59 . doi : 10.2298/PIM0694059B. http://geodesic.mathdoc.fr/articles/10.2298/PIM0694059B/

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