In this paper, we prove an inequality, which we call " Devroye inequality " , for a large class of non-uniformly hyperbolic dynamical systems (M, f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and Hénon-like maps. Devroye inequality provides an upper bound for the variance of ...
