Large Deviations For A General-Class Of Random Vectors

RS Ellis, University of Massachusetts - Amherst

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The published version is located at http://www.jstor.org/stable/info/2243592

Abstract

This paper proves large deviation theorems for a general class of random vectors taking values in 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.