Principe de grandes déviations autonormalisées pour des chaı̂nes de Markov

Abstract

We prove a self-normalized large deviation principle for sums of Banach space valued functions of a Markov chain. Self-normalization applies to situations for which a domination hypothesis would be necessary in order to obtain a full large deviation principle. We follow the lead of Dembo and Shao [2] who state partial large deviations principles for independent and identically distributed random sequences.