## The Annals of Probability

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

Richard S. Ellis

#### 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

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