Deviation and concentration inequalities for dynamical systems with subexponential decay of correlation

Christophe Cuny (1) , Jérôme Dedecker (2) , Florence Merlevède (3)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.

Mots clés: Large deviations; Moderate deviations; Nonuniformly expanding maps; Young towers

Domaines: Probabilités [math.PR]

Christophe Cuny, Jérôme Dedecker, Florence Merlevède. Deviation and concentration inequalities for dynamical systems with subexponential decay of correlation. Stochastics and Dynamics, 2023, ⟨10.1142/S0219493723500259⟩. ⟨hal-03540444⟩