A note on the rate of convergence in the martingale central limit theorem (Q794054)

Applying the Skorokhod embedding scheme \textit{C. C. Heyde} and \textit{B. M. Brown} [Ann. Math. Stat. 41, 2161-2165 (1970; Zbl 0225.60026)] obtained an estimate of the rate of convergence in the central limit theorem for martingale differences with finite absolute moments of order \(2+2\delta\) for \(0<\delta \leq 1\). In the present note this estimate is extended to the range \(1<\delta<\infty\) (up to a logarithmic factor). The method of proof is a refinement of the classical Lindeberg-Lévy approach developed by \textit{E. Bolthausen}, Ann. Probab. 10, 672-688 (1982; Zbl 0494.60020).