## The Annals of Probability

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

### Large Deviations of Sums of Independent Random Variables

#### 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**

https://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. https://projecteuclid.org/euclid.aop/1176994938