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

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

2004-03-23

arxiv.org/abs/math/0403385v1

Mathematics

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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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