Exact convergence rates in the central limit theorem for a class of martingales

Mohamed El Machkouri; Lahcen Ouchti

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Exact convergence rates in the central limit theorem for a class of martingales

Mohamed El Machkouri·Lahcen Ouchti

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Abstract

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the rate $n^{-1/2}\log n$ is reached. We give interesting examples of martingales with unbounded increments which belong to the considered class.

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Mohamed El Machkouri, Lahcen Ouchti. 2004-03-23. Exact convergence rates in the central limit theorem for a class of martingales. https://arxiv.org/abs/math/0403385

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