Moment bounds for dependent sequences in smooth Banach spaces

Abstract

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 $\{T,T^2,\cdots ,T^n\}$, on a class of smooth functions, when $T$ belongs to a class of nonuniformly expanding maps of the unit interval.

27 pages