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

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

2010-06-16

arxiv.org/abs/1006.3164v1

Mathematics

Probability

12 pages

Scientific paper

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.

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