About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Volný, Dalibor
A nonergodic version of Gordin's CLT for integrable stationary processes. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 28 (1987), issue 3, pp. 413-419
MSC: 28D05, 60F05, 60G10, 60G42 | MR 912569 | Zbl 0629.60030
References:
[1] P. BILLINGSLEY: Ergodic Theory and Information. Wiley, New York, 1965. MR 0192027 | Zbl 0141.16702
[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 0780729
[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 0251785 | Zbl 0212.50005
[5] P. HALL C. C. HEYDE: Martingale Limit Theory and its Applications. Academic Press, New York, 1980. MR 0624435
[6] N. HERRHDORF: Stationary strongly mixing sequences not satisfying the central limit theorem. Ann. Probability 11 (1983), 809-813. MR 0704571
[7] M. LOЀVE: Probability Theory. Van Nostrand, New York, 1955. MR 0203748
[8] J. C. OXTOBY: Ergodic sets. Bulletin of the Amer. Math. Soc. 58 (1952), 116-136. MR 0047262 | Zbl 0046.11504
[9] W. F. STOUT: The Hartman-Wintner law of the iterated logarithm for martingales. Ann. Math. Statist. 41 (1970), 2158-2160. Zbl 0235.60046
[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.
Partner of
EuDML logo