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On the probability of large deviations of sums of independent identically distributed random variables. (English. Russian original) Zbl 0552.60023

Sov. Math., Dokl. 28, 639-644 (1983); translation from Dokl. Akad. Nauk SSR 273, 301-306 (1983).
Let \(V_ n\) be the distribution function of the sum of n independent identically distributed random variables with zero mean and unit variance. Let \(\Phi\) be the standard normal distribution function. This note describes results that fall into the usual large deviation framework. They deal with the behaviour of the ratio \((1-V_ n(x))/(1- \Phi (x/\sqrt{n}))\) as \(n\to \infty\) for \(0<x\leq \Lambda (\sqrt{n})\) where \(\Lambda\) (z)/z\(\uparrow \infty\), and \(\Lambda (z)/z^{1+\delta}\downarrow\) for some \(\delta <1\). The results themselves are too complex to summarise here.
Reviewer: J.D.Biggins

MSC:

60F10 Large deviations
60G50 Sums of independent random variables; random walks
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