A nonuniform bound on the rate of convergence in the martingale central limit theorem (Q1110183)

The main result of the paper is a sharp nonuniform bound of the rate of convergence in the central limit theorem for martingale differences having finite moments of order 2-2\(\delta\) for some \(0<\delta <\infty\). The method of the proof is the ``nonuniform'' modification of the first author's version of the iterative method developed by Bolthausen [Ann. Probab. 16, No.1, 275-299 (1988; Zbl 0639.60030)]. A nonuniform bound for the rate of convergence of discrete-time martingales to mixtures of normal distributions is obtained as a consequence of the main result.