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February, 1984 Large Deviations for a General Class of Random Vectors
Richard S. Ellis
Ann. Probab. 12(1): 1-12 (February, 1984). DOI: 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.

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Richard S. Ellis. "Large Deviations for a General Class of Random Vectors." Ann. Probab. 12 (1) 1 - 12, February, 1984. https://doi.org/10.1214/aop/1176993370

Information

Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0534.60026
MathSciNet: MR723726
Digital Object Identifier: 10.1214/aop/1176993370

Subjects:
Primary: 60F10
Secondary: 26A51‎

Keywords: entropy function , exponential convergence , Large deviation property

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February, 1984
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