Moderate deviations for stationary sequences of Hilbert valued bounded random variables

Sophie Dede (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are martingale approximations and a new Hoeffding inequality for non adpated sequences of Hilbert-valued random variables. Applications to Cramer-Von Mises statistics, functions of linear processes and stable Markov chains are given.

Mots clés: stationary processes; Hilbert space; moderate deviations; martingale approximation; stationary processes.

Domaines: Probabilités [math.PR]

Sophie Dede. Moderate deviations for stationary sequences of Hilbert valued bounded random variables. Journal of Mathematical Analysis and Applications, 2009, 349 (2), pp.374-394. ⟨hal-00280709v2⟩