@article{CMUC_1987_28_3_a1,
author = {Voln\'y, Dalibor},
title = {A nonergodic version of {Gordin's} {CLT} for integrable stationary processes},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {413--419},
year = {1987},
volume = {28},
number = {3},
mrnumber = {912569},
zbl = {0629.60030},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1987_28_3_a1/}
}
Volný, Dalibor. A nonergodic version of Gordin's CLT for integrable stationary processes. Commentationes Mathematicae Universitatis Carolinae, Tome 28 (1987) no. 3, pp. 413-419. http://geodesic.mathdoc.fr/item/CMUC_1987_28_3_a1/
[1] P. BILLINGSLEY: Ergodic Theory and Information. Wiley, New York, 1965. | MR | Zbl
[2] C. G. ESSEEN S. JANSON: On moment conditions for normed sums of independent variables and martingale differences. Stoch. proc. and their appl. 19 (1985), 173-182. | MR
[3] M. I. GORDIN: Abstracts of communications. T.1: A-K, International conference on probability theory, Vilnius, 1973.
[4] M. I. GORDIN: The central limit theorem for stationary processes. Soviet Math. Dokl. 10 (1969), 1174-1176. | MR | Zbl
[5] P. HALL C. C. HEYDE: Martingale Limit Theory and its Applications. Academic Press, New York, 1980. | MR
[6] N. HERRHDORF: Stationary strongly mixing sequences not satisfying the central limit theorem. Ann. Probability 11 (1983), 809-813. | MR
[7] M. LOЀVE: Probability Theory. Van Nostrand, New York, 1955. | MR
[8] J. C. OXTOBY: Ergodic sets. Bulletin of the Amer. Math. Soc. 58 (1952), 116-136. | MR | Zbl
[9] W. F. STOUT: The Hartman-Wintner law of the iterated logarithm for martingales. Ann. Math. Statist. 41 (1970), 2158-2160. | Zbl
[10] D. VOLNÝ: The central limit problem for strictly stationary sequences. Ph.D. thesis 1984, Mathematical Institute, Charles university, Prague (in Czech).
[11] D. VOLNÝ: Approximation of stationary processes and the central limit problem. Proceedings of the Japan-USSR Symposium on probability theory, Kyoto (1986).
[12] D. VOLNÝ R. YOKOYAMA: On the law of iterated logarithm for martingales. submitted for publication.