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

Autor:	Borovkov, A. A., Borovkov, K. A.
Rok vydání:	2010
Předmět:	Mathematics - Probability Mathematics - Classical Analysis and ODEs 60F10 (Primary) 26A12 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1006.3164 Zobrazit plný text záznamu View this record from Arxiv