An example on the central limit theorem for associated sequences. (English) Zbl 0544.60033

Herrndorf, Norbert

Ann. Probab. 12, 912-917 (1984).

C. M. Newman [Commun. Math. Phys. 74, 119-128 (1980; Zbl 0429.60096)] and C. M. Newman and A. L. Wright [Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009)] conjectured that the central limit theorem holds for strictly stationary associated sequences \((X_ n)\) with \(K(R)=Var(X_ 1)+2\sum^{R}_{j=2}Cov(X_ 1,X_ j)\) slowly varying as \(R\to \infty\). The content of this paper is a counterexample to this conjecture.

MSC:

60F05

Central limit and other weak theorems

Keywords:

central limit theorem; stationary associated sequences

Citations:

Zbl 0429.60096; Zbl 0465.60009