ON SOME EXTENSIONS OF KARAMATA'S THEORY AND THEIR APPLICATIONS

Abstract

This is a survey of the authors' results on the properties and appli- cations of some subclasses of (so-called) O-regularly varying (ORV) functions. In particular, factorization and uniform convergence theorems for Avaku- movic-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 func- tions. Applications are given concerning the asymptotic behavior of solutions of certain stochastic differential equations.