Kir’yanova, L. V.; Rotar’, V. I. On the convergence rate in the central limit theorem for a martingale. (Russian) Zbl 0739.60017 Probabilistic problems in discrete mathematics, Interuniv. Collect., Moskva, 136-140 (1988). [For the entire collection see Zbl 0702.00027.]The authors obtain the exact combined upper bound for the rate of convergence in the central limit theorem for martingales. In general, the rate has the order \(n^{-1/4}\) which cannot be improved. But for the i.i.d. case the upper bound coincides with the well-known Berry-Esseen estimate of the order \(n^{-1/2}\). Reviewer: I.S.Borisov (Novosibirsk) Cited in 1 Review MSC: 60F05 Central limit and other weak theorems 60G42 Martingales with discrete parameter Keywords:Lindeberg’s operator method; rate of convergence; central limit theorem for martingales; Berry-Esseen estimate Citations:Zbl 0702.00027 PDFBibTeX XMLCite \textit{L. V. Kir'yanova} and \textit{V. I. Rotar'}, in: A scheme of arrangement and evolution of particles. . 136--140 (1988; Zbl 0739.60017)