Dalibor Volný
Published 2008-05-08Version 1
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.
Central limit theorem for stationary linear processes
A strictly stationary, "causal," 5-tuplewise independent counterexample to the central limit theorem
Central limit theorem for multiplicative class functions on the symmetric group
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