A random functional central limit theorem for stationary linear processes generated by martingales

Statistics and Probability Letters

Volumn 35, Issue 4, 1997, Pages 417-422

  Fakhre Zakeri, Issa ^a   Lee, Sangyeol ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b Sookmyung Women's University   (South Korea)

Author keywords

Functional central limit theorem; Linear process; Martingales; Mixing in the sense of Renyi; Random indices; Stationary

Indexed keywords

EID: 0031280737     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(97)00040-0     Document Type: Article

References (10)

1. Aldous, D.J., Eagleson, G.K., 1978. On mixing and stability of limit theorems. Ann. Probab. 6, 325-331.
2. Babu, G.J., Ghosh, M., 1976. A random functional central limit theorem for martingales. Acta. Math. Acad. Sci. Hungar. 27, 301-306.
3. Billingsley, P., 1968. Convergence of Probability Measures. Wiley, New York.
4. Csörgö, M., Fischler, M., 1973. Some examples and results in the theory of mixing and random-sum central limit theorems. Period. Math. Hungar, 3, 41-57.
5. Fakhre-Zakeri, Farshidi, J., 1993. A central limit theorem with random indices for stationary linear processes. Statist. Probab. Lett. 17, 91-95.
6. Fotopoulous, S.B., 1991. On the speed of convergence of the distribution of random sum of weighted independent variables. Sequential Anal. 10, 17-26.
7. Hall, P., Heyde, C.C., 1980, Martingale Limit Theorey and Its Applications. Academic Press, New York.
8. Hannan, E.J., 1970. Multivariate Time Series. Wiley, New York.
9. Hannan, E.J., Heyde, C.C., 1972. On limit theorems for quadratic functions of discrete time-series. Ann. Math. Statist. 43, 2058-2066.
10. Rootzén, H., 1974. Rényi-mixing and functional limit theorems for martingales. Trans. of the 7th Prague Conf. on Information Theory, Statistical Decision Functions, Random Processes. Vol. 4, pp. 505-513.