On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence

Large Deviations Bounds for Non-uniformly Hyperbolic Maps and Weak Gibbs Measures

We establish bounds for the measure of deviation sets associated to continuous observables with respect to weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms.

A Course on Large Deviations with an Introduction to Gibbs Measures

Large Deviations of Divergence Measures on Partitions

We discuss Chernoo-type large deviation results for the total variation , the I-divergence errors, and the 2-divergence errors on partitions. In contrast to the total variation and the I-divergence, the 2-divergence has an unconventional large deviation rate. Applications to Bahadur eeciencies of goodness-of-t tests based on these divergence measures for multivariate observations are given.

Large deviations for bootstrapped empirical measures

We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and the observations. As an application we recover known conditional and unconditional LDPs and obtain some new ones.

Large Deviations for Symmetrised Empirical Measures

In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures 1 n Pn i=1 δ(Xn i ,X n σn(i) ) where σn is a random permutation and ((X i )1≤i≤n)n≥1 is a triangular array of random variables with suitable properties. As an application we show how this result allows to improve the Large Deviation Principles for symmetrised initial-terminal conditions bridge ...