ON A FUNCTIONAL CENTRAL LIMIT THEOREM FOR THE LINEAR PROCESS GENERATED BY ASSOCIATED RANDOM VARIABLES IN A HILBERT SPACE

Title & Authors
ON A FUNCTIONAL CENTRAL LIMIT THEOREM FOR THE LINEAR PROCESS GENERATED BY ASSOCIATED RANDOM VARIABLES IN A HILBERT SPACE
Ko, Mi-Hwa; Kim, Tae-Sung;

Abstract
Let {$\small{{\xi}_k,\;k\;{\in}\;{\mathbb{Z}}}$} be a strictly stationary associated sequence of H-valued random variables with \$E{\xi}_k\;
Keywords
functional central limit theorem;linear process in a Hilbert space;association;linear operator;Hilbert space-valued random variable;
Language
English
Cited by
1.
Precise asymptotics for the linear processes generated by associated random variables in Hilbert spaces, Computers & Mathematics with Applications, 2012, 64, 6, 1937
References
1.
R. E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing : Probability models Holt, Rinehart and Winston, New York, 1975

2.
P. Billingsley, Convergence of Probability, John Wiley, New York, 1968

3.
D. Bosq, Linear Processes in Function Spaces, Lectures Notes in Statistics, 149, Springer, Berlin, 2000

4.
D. Bosq, Berry-Esseen inequality for linear processes in Hilbert spaces, Statist. Probab. Letters 63 (2003), 243-247

5.
P. Brockwell and R. Davis, Time Series, Theory and Method. Springer, Berlin, 1987

6.
R. A. R. Burton and H. Dehling, An invariance principle for weakly associated random vectors, Stochastic Processes Appl. 23 (1986), 301-306

7.
J. T. Cox and G. Grimmett, Central limit theorems for associated random variables and the percolation model, Ann. Probab. 12 (1984), 514-528

8.
N. A. Denisevskii and Y. A. Dorogovtsev, On the law of large numbers for a linear process in Banach space, Soviet Math. Dokl. 36 (1988), no. 1, 47-50

9.
T. S. Kim, M. H. Ko, and S. M. Chung, A central limit theorem for the stationary multivariate linear processes generated by associated random vectors, Commun. Korean Math. Soc. 17 (2002), no. 1, 95-102

10.
T. S. Kim and M. H. Ko, On a functional central limit theorem for stationary linear processes generated by associated processes, Bull. Korean Math. Soc. 40 (2003), no. 4, 715-722

11.
C. M. Newman, Normal fluctuations and the FKG inequalities, Comm. Math. Phys. 74 (1980), 119-128

12.
C. M. Newman and A. L. Wright, An invariance principle for certain dependent sequences, Ann. Probab. 9 (1981), 671-675