The Annals of Probability

Large Deviations of Sums of Independent Random Variables

S. V. Nagaev

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Abstract

This paper deals with numerous variants of bounds for probabilities of large deviations of sums of independent random variables in terms of ordinary and generalized moments of individual summands. A great deal of attention is devoted to the study of the precision of these bounds. In this connection comparisons are made with precise asymptotic results. At the end of the paper various applications of the bounds for probabilities of large deviations to the strong law of large numbers, the central limit theorem and to certain other problems are discussed.

Article information

Source
Ann. Probab. Volume 7, Number 5 (1979), 745-789.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176994938

Digital Object Identifier
doi:10.1214/aop/1176994938

Mathematical Reviews number (MathSciNet)
MR542129

Zentralblatt MATH identifier
0418.60033

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
Inequalities large deviations sums of independent random variables strong law of large numbers central limit theorem moments

Citation

Nagaev, S. V. Large Deviations of Sums of Independent Random Variables. Ann. Probab. 7 (1979), no. 5, 745--789. doi:10.1214/aop/1176994938. http://projecteuclid.org/euclid.aop/1176994938.


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