Stationary Strongly Mixing Sequences Not Satisfying the Central Limit Theorem

Herrndorf, Norbert

Ann. Probab., Tome 11 (1983) no. 4, p. 809-813 / Harvested from Project Euclid

Résumé

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.

Publié le : 1983-08-14
Classification: Central limit theorem, strongly mixing strictly stationary sequences, 60F05, 60G10

@article{1176993529,
     author = {Herrndorf, Norbert},
     title = {Stationary Strongly Mixing Sequences Not Satisfying the Central Limit Theorem},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 809-813},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993529}
}

Herrndorf, Norbert. Stationary Strongly Mixing Sequences Not Satisfying the Central Limit Theorem. Ann. Probab., Tome 11 (1983) no. 4, pp.  809-813. http://gdmltest.u-ga.fr/item/1176993529/