Central Limit Theorems revisited

Statistics and Probability Letters

Volumn 47, Issue 3, 2000, Pages 265-275

  Kundu, Subrata ^a   Majumdar, Suman ^b   Mukherjee, Kanchan ^c  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Central Limit Theorem; Hilbert space; Lindeberg condition; Martingale difference array; Primary 60F05; Secondary 60B12; Weak convergence

Indexed keywords

EID: 0010440018     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(99)00164-9     Document Type: Article

References (13)

1. Araujo, A., Giné, E., 1980. The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.
2. Basu A.K. Uniform and nonuniform estimates in the clt for Banach valued dependent random variables. J. Multivariate Anal. 25:1988;153-163.
3. Chung, K.L., 1970. A Course in Probability Theory. Academic Press, New York.
4. Dunford, N., Schwartz, J.T., 1958. Linear Operators. Part I: General Theory. Wiley Classics Library Edition 1988. Wiley, New York.
5. Enflo P. A counter-example to the approximation problem in Banach spaces. Acta Math. 103:1973;309-317.
6. Fabian, V., Hannan, J., 1985. Introduction to Probability and Mathematical Statistics. Wiley, New York.
7. Gaenssler, P., Haeusler, E., 1986. On martingale central limit theory. In: Taqqu, M., Eberlein, E. (Eds.), Dependence in Probability and Statistics; A Survey of Recent Results. Birkhauser, Boston.
8. Garling D.J.H. Functional central limit theorems in Banach spaces. Ann. Probab. 4:1976;600-611.
9. Hall, P., Heyde, C.C., 1980. Martingale Limit Theory and Its Applications. Academic Press, New York.
10. Helland I.S. Central limit theorems for martingales with discrete or continuous time. Scand. J. Statist. 9:1982;79-94.
11. Parthasarathy, K.R., 1967. Probability Measures on Metric Spaces. Academic Press, New York.
12. Pollard, D., 1984. Convergence of Stochastic Processes. Springer, New York.
13. Xie Y. Limit theorems of Hilbert valued semimartingales and Hilbert valued martingale measures. Stochastic Process. Appl. 59:1995;277-295.