Certain non-uniform rates of convergence to normality for martingale differences (Q5903389)

This paper provides non-uniform bounds on the departure from normality for sums of martingale differences for which the uniform boundedness of the conditional m.g.f.'s of the differences in a neighbourhood of zero is assumed. It is also assumed that either the conditional variances of the martingale differences are a.s. constant or the differences themselves are bounded. The results supplement those of \textit{E. Bolthausen}, Ann. Probab. 10, 672-688 (1982; Zbl 0494.60020), and embedding techniques are avoided in the proofs. Corollaries on convergence of absolute moments and probabilities of moderate deviations are also given.