## The Annals of Probability

- Ann. Probab.
- Volume 12, Number 1 (1984), 1-12.

### Large Deviations for a General Class of Random Vectors

#### Abstract

This paper proves large deviation theorems for a general class of random vectors taking values in $\mathbb{R}^d$ and in certain infinite dimensional spaces. The proofs are based on convexity methods. As an application, we give a new proof of the large deviation property of the empirical measures of finite state Markov chains (originally proved by M. Donsker and S. Varadhan). We also discuss a new notion of stochastic convergence, called exponential convergence, which is closely related to the large deviation results.

#### Article information

**Source**

Ann. Probab., Volume 12, Number 1 (1984), 1-12.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993370

**Digital Object Identifier**

doi:10.1214/aop/1176993370

**Mathematical Reviews number (MathSciNet)**

MR723726

**Zentralblatt MATH identifier**

0534.60026

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F10: Large deviations

Secondary: 26A51: Convexity, generalizations

**Keywords**

Large deviation property entropy function exponential convergence

#### Citation

Ellis, Richard S. Large Deviations for a General Class of Random Vectors. Ann. Probab. 12 (1984), no. 1, 1--12. doi:10.1214/aop/1176993370. https://projecteuclid.org/euclid.aop/1176993370