Research papers

Estimates of Berry–Esseen type for probabilities of large deviations under violation of Cramér condition

A. I. Sakhanenko

Ugra State University, Khanty-Mansiysk, Russia

Abstract: Two-sided estimates for probabilities of large deviations for sums of independent random variables with finite variances are obtained. All asymptotics of the probabilities are described in terms of deviation function $\Lambda(x,y)$ of a sum of truncated random variables. All error terms are explicitly estimated by a modified Lyapunov ratio $L(H(x),y)$.

Keywords: probabilities of large deviations, deviation function, Lyapunov ratio.

UDC: 519.214.4

MSC: 60F10

Received December 20, 2008, published July 15, 2009

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