Self-normalized large deviations for Markov chains
Résumé
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 Shoo [2] who state partial large deviations Principles for independent and identically distributed random sequences. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.