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October, 1979 Large Deviations of Sums of Independent Random Variables
S. V. Nagaev
Ann. Probab. 7(5): 745-789 (October, 1979). DOI: 10.1214/aop/1176994938


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.


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S. V. Nagaev. "Large Deviations of Sums of Independent Random Variables." Ann. Probab. 7 (5) 745 - 789, October, 1979.


Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0418.60033
MathSciNet: MR542129
Digital Object Identifier: 10.1214/aop/1176994938

Primary: 60F10
Secondary: 60G50

Keywords: central limit theorem , Inequalities‎ , large deviations , moments , Strong law of large numbers , Sums of independent random variables

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 5 • October, 1979
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