Level-2 Large Deviations for I.I.D. Random Vectors
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].
KeywordsRandom Vector Entropy Function Borel Probability Measure Contraction Principle Compact Convex Subset
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