## The Annals of Probability

- Ann. Probab.
- Volume 12, Number 3 (1984), 903-906.

### Convexity and Large Deviations

#### Abstract

A convexity argument is used to establish a representation formula from which one can derive the asymptotics of large deviations of sums of i.i.d. random variables on $\mathbb{R}^d$. This simplifies a proof in [4] which relied on fixed point and probabilistic arguments.

#### Article information

**Source**

Ann. Probab., Volume 12, Number 3 (1984), 903-906.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993239

**Digital Object Identifier**

doi:10.1214/aop/1176993239

**Mathematical Reviews number (MathSciNet)**

MR744245

**Zentralblatt MATH identifier**

0543.60035

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G10: Stationary processes

Secondary: 60G50: Sums of independent random variables; random walks

**Keywords**

Large deviations convexity

#### Citation

Ney, Peter. Convexity and Large Deviations. Ann. Probab. 12 (1984), no. 3, 903--906. doi:10.1214/aop/1176993239. https://projecteuclid.org/euclid.aop/1176993239