On an Extension of the Concept of Slowly Varying Function with Applications to Large Deviation Limit Theorems

Abstract

Karamata's integral representation for slowly varying functions is extended to a broader class of the so-called $\psi$-locally constant functions, i.e. functions $f(x)>0$ having the property that, for a given non-decreasing function $\psi (x)$ and any fixed $v$, $f(x+v\psi (x))/f(x)\to 1$ as $x\to \infty$. We consider applications of such functions to extending known results on large deviations of sums of random variables with regularly varying distribution tails.

arXiv comment12 pages

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