Non-uniform Berry-Esseen theorem and Edgeworth expansions with applications to transport distances for weakly dependent random variables

Abstract: We obtain non-uniform Berry-Esseen type estimates and Edgeworth expansions for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding dynamical systems, products of random matrices and some classes of local statistics.