Moment bounds for dependent sequences in smooth Banach spaces

Jérôme Dedecker (1) , Florence Merlevède (2)

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

We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of {T, T^2, ..., T^n}, on a class of smooth functions, when T belongs to a class of nonuniformly expanding maps of the unit interval.

Mots clés: Moment inequalities; Smooth Banach spaces; Empirical process; Young towers; Wasserstein distance

Domaines: Probabilités [math.PR]

Jérôme Dedecker, Florence Merlevède. Moment bounds for dependent sequences in smooth Banach spaces. Stochastic Processes and their Applications, 2015, 125 (9), pp.3401-3429. ⟨hal-00971755⟩