| Title:
|
A nonergodic version of Gordin's CLT for integrable stationary processes (English) |
| Author:
|
Volný, Dalibor |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
1987 |
| Pages:
|
413-419 |
| . |
| Category:
|
math |
| . |
| MSC:
|
28D05 |
| MSC:
|
60F05 |
| MSC:
|
60G10 |
| MSC:
|
60G42 |
| idZBL:
|
Zbl 0629.60030 |
| idMR:
|
MR912569 |
| . |
| Date available:
|
2008-06-05T21:29:36Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106553 |
| . |
| Reference:
|
[1] P. BILLINGSLEY: Ergodic Theory and Information.Wiley, New York, 1965. Zbl 0141.16702, MR 0192027 |
| Reference:
|
[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 |
| Reference:
|
[3] M. I. GORDIN: Abstracts of communications.T.1: A-K, International conference on probability theory, Vilnius, 1973. |
| Reference:
|
[4] M. I. GORDIN: The central limit theorem for stationary processes.Soviet Math. Dokl. 10 (1969), 1174-1176. Zbl 0212.50005, MR 0251785 |
| Reference:
|
[5] P. HALL C. C. HEYDE: Martingale Limit Theory and its Applications.Academic Press, New York, 1980. MR 0624435 |
| Reference:
|
[6] N. HERRHDORF: Stationary strongly mixing sequences not satisfying the central limit theorem.Ann. Probability 11 (1983), 809-813. MR 0704571 |
| Reference:
|
[7] M. LOЀVE: Probability Theory.Van Nostrand, New York, 1955. MR 0203748 |
| Reference:
|
[8] J. C. OXTOBY: Ergodic sets.Bulletin of the Amer. Math. Soc. 58 (1952), 116-136. Zbl 0046.11504, MR 0047262 |
| Reference:
|
[9] W. F. STOUT: The Hartman-Wintner law of the iterated logarithm for martingales.Ann. Math. Statist. 41 (1970), 2158-2160. Zbl 0235.60046 |
| Reference:
|
[10] D. VOLNÝ: The central limit problem for strictly stationary sequences.Ph.D. thesis 1984, Mathematical Institute, Charles university, Prague (in Czech). |
| Reference:
|
[11] D. VOLNÝ: Approximation of stationary processes and the central limit problem.Proceedings of the Japan-USSR Symposium on probability theory, Kyoto (1986). |
| Reference:
|
[12] D. VOLNÝ R. YOKOYAMA: On the law of iterated logarithm for martingales.submitted for publication. |
| . |
