LARGE AND MODERATE DEVIATIONS FOR BOUNDED FUNCTIONS OF SLOWLY MIXING MARKOV CHAINS

J Dedecker (1) , Sébastien Gouëzel (2) , F Merlevède (3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.

Domaines: Probabilités [math.PR]

J Dedecker, Sébastien Gouëzel, F Merlevède. LARGE AND MODERATE DEVIATIONS FOR BOUNDED FUNCTIONS OF SLOWLY MIXING MARKOV CHAINS. Stochastics and Dynamics, 2018, 2018 (2), pp.1850017. ⟨hal-01347288⟩