A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem

Abstract

The main result of the present paper is a sharp nonuniform bound on the rate of convergence to normality in the central limit theorem for martingales having finite moments of order $2 + 2\delta$ for some $0 < \delta < \infty$. A nonuniform bound on the rate for convergence to mixtures of normal distributions is obtained as a consequence.