Exactness of martingale approximation and the central limit theorem

Details Exactness of martingale approximation and the central limit theorem Exactness of martingale approximation and the central limit theorem

2008-05-08

arxiv.org/abs/0805.1198v1

Mathematics

Probability

Scientific paper

The article is showing sharpness of central limit theorems of Kipnis and Varadhan, Derriennic and Lin, Maxwell and Woodroofe. In the case of the CLT of Derriennic and Lin (for Markov chains with a normal operator) it is shown that the assumption of normality cannot be relaxed. In the case of the CLT of Maxwell and Woodroofe, the example of Peligrad and Utev is improved in the sense of getting a convergence to different laws.

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