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Level-2 Large Deviations for I.I.D. Random Vectors

  • Richard S. Ellis
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 271)

Abstract

Theorem II.4.3 stated the level-2 large deviation property for i.i.d. random vectors taking values in ℝ d . This theorem follows from the results contained in Donsker and Varadhan (1975a, 1976a), which prove level-2 large deviation properties for Markov processes taking values in a complete separable metric space.1 In Chapter VIII, we will give an elementary, self-contained proof of Theorem I1.4.3 in the special case of i.i.d. random variables with a finite state space. This version of the theorem was applied in Chapter III to study the exponential convergence of velocity observables for the discrete ideal gas with respect to the microcanonical ensemble [Theorem III.4.4].

Keywords

Random Vector Entropy Function Borel Probability Measure Contraction Principle Compact Convex Subset 
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Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Richard S. Ellis
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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