%0 Journal Article
%T On the central and local limit theorem for martingale difference sequences
%A Mohamed El Machkouri
%A Dalibor Volny
%J Mathematics
%D 2004
%I arXiv
%X Let $(\Omega, \A, \mu)$ be a Lebesgue space and $T$ an ergodic measure preserving automorphism on $\Omega$ with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on $\Omega$ with a common non-degenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.
%U http://arxiv.org/abs/math/0403008v1