Large Deviations for a General Class of Random Vectors
Open Access
- 1 February 1984
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 12 (1), 1-12
- https://doi.org/10.1214/aop/1176993370
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.