The functional central limit theorem under the strong mixing condition

Annals of Probability

Volumn 28, Issue 3, 2000, Pages 1336-1352

  Merlevède, Florence ^a   Peligrad, Magda ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF CINCINNATI   (United States)

Author keywords

Central limit theorem; Quantiles; Strong mixing; Weak invariance principle

Indexed keywords

EID: 0034214586     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. BRADLEY, R. C. (1997). On quantiles and the central limit theorem question for strongly mixing sequences. J. Theoret. Probab. 10 507-555.
3. DEHLING, H., DENKER, M. and PHILIPP, W. (1986). Central limit theorems for mixing sequences of random variables under minimal conditions. Ann. Probab. 14 1359-1370.
4. DENKER, M. (1986). Uniform integrability and the central limit theorem for strongly mixing processes. In Dependence in Probability and Statistics. A Survey of Recent Results (E. Eberlein and M. S. Taqqu, eds.). Birkhäuser, Boston.
5. DOUKHAN, P., MASSART, P. and RIO, E. (1994). The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 30 63-82.
6. HALL, P. and HEYDE, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York.
7. HERRNDORF, N. (1985). A functional central limit theorem for strongly mixing sequences of random variables. Z. Wahrsch. Verw. Gebiete 69 541-550.
8. IBRAGIMOV, I. A. (1962). Some limit theorems for stationary processes. Teor. Verojatnost. i Primenen. 7 361-392.
9. IBRAGIMOV, I. A. and LINNIK, Yu. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters-Noorhoff, Groningen.
10. IBRAGIMOV, I. A. and ROZANOV, IU. A. (1978). Gaussian Random Processes. Springer, Berlin.
11. MORI, T. and YOSHIHARA, K. (1986). A note on the central limit theorem for stationary strong-mixing sequences. Yokohama Math J. 35 143-146.
12. PELIGRAD, M. (1986). Recent advances in the central limit theorem and its weak invariance principles for mixing sequences of random variables. In Dependence in Probability and statistics. A Survey of Recent Results (E. Eberlein and M. S. Taqqu, eds.). Birkhäuser, Boston.
13. PELIGRAD, M. (1992). On the central limit theorem for decomposed strong mixing sequences. Stochastic Process Appl. 42 181-193.
14. RIO, E. (1993). Covariance inequalities for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 29 587-597.
15. RIO, E. (1995). The functional law of the iterated logarithm for stationary strongly mixing sequences. Ann. Probab. 23 1188-1203.
16. RIO, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants. In Mathématiques et Applications de la SMAI. 31. Springer, Berlin.
17. ROSENBLATT, M. (1956). A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. U.S.A. 42 43-47.