标题： 鞅逼近的精确性与中心极限定理 显示英文标题

标题： Exactness of martingale approximation and the central limit theorem

摘要： 文章展示了Kipnis和Varadhan、Derriennic和Lin、Maxwell和Woodroofe的中心极限定理的精确性。在Derriennic和Lin的CLT（对于具有正规算子的马尔可夫链）情况下，证明了正规性的假设不能被放松。在Maxwell和Woodroofe的CLT情况下，Peligrad和Utev的例子在得到收敛到不同分布的意义上得到了改进。 显示英文摘要

摘要： 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.