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August, 1983 Stationary Strongly Mixing Sequences Not Satisfying the Central Limit Theorem
Norbert Herrndorf
Ann. Probab. 11(3): 809-813 (August, 1983). DOI: 10.1214/aop/1176993529


For every sequence $(\varepsilon_n)_{n \in N}$ in (0, 1) there exists a strictly stationary orthonormal sequence $(X_n)_{n \in N}$ of random variables with $|P(A \cap B) - P(A)P(B)| \leq \varepsilon_n$ for all $A \in \sigma(X_1, \cdots, X_k), B \in \sigma(X_{k+n}, X_{k+n+1}, \cdots), k \in \mathbb{N}, n \in \mathbb{N}$, such that the distribution of $n^{-1/2} \sum^n_{i=1} X_i$ is not weakly convergent to the standard normal distribution.


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Norbert Herrndorf. "Stationary Strongly Mixing Sequences Not Satisfying the Central Limit Theorem." Ann. Probab. 11 (3) 809 - 813, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0513.60033
MathSciNet: MR704571
Digital Object Identifier: 10.1214/aop/1176993529

Primary: 60F05
Secondary: 60G10

Keywords: central limit theorem , strongly mixing strictly stationary sequences

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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