Moderate deviations for stationary sequences of Hilbert valued bounded random variables

Details Moderate deviations for stationary sequences of Hilbert valued bounded random variables Moderate deviations for stationary sequences of Hilbert valued bounded random variables

2008-05-19

arxiv.org/abs/0805.2899v2

Journal of Mathematical Analysis and applications Volume 349, Issue 2 (2009) 374-394

Mathematics

Probability

Scientific paper

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.

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