Certain non-uniform rates of convergence to normality for a restricted class of martingales

Abstract

Non-uniform rates of convergence to normality are derived for standardized sums of random variables which form a martingale difference array, with the sum of conditional variances being a constant in each row. As a consequence, we obtain probabilities of moderate deviations, convergence of absolute moments and (nonuniform) L p versions of the Berry-Esseen theorem.