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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 \(n^{-1/2}\).

MSC:

60F05 Central limit and other weak theorems
60G42 Martingales with discrete parameter

Citations:

Zbl 0702.00027
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