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November, 1985 On the Central Limit Question Under Absolute Regularity
Richard C. Bradley
Ann. Probab. 13(4): 1314-1325 (November, 1985). DOI: 10.1214/aop/1176992815


Davydov showed that in a classic central limit theorem of Ibragimov under the strong mixing condition, the combinations of mixing rate and moment assumption were practically as weak as permissible. Here some constructions will be given to show that Davydov's observation still holds under the additional assumption that the growth of $\operatorname{var}(X_1 + \cdots + X_n)$ be asymptotically linear. Our constructions will be similar to a recent one of Herrndorf.


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Richard C. Bradley. "On the Central Limit Question Under Absolute Regularity." Ann. Probab. 13 (4) 1314 - 1325, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0582.60047
MathSciNet: MR806228
Digital Object Identifier: 10.1214/aop/1176992815

Primary: 60G10
Secondary: 60F05

Keywords: absolute regularity , central limit theorem , Strong mixing

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
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