THE ALMOST SURE CONVERGENCE OF AANA SEQUENCES IN DOUBLE ARRAYS

Ko Mi-Hwa; Ryu Dae-Hee; Kim Tae-Sung

doi:10.4134/BKMS.2006.43.1.169

HOME > Journal Browse > About Journal > Journal Vol & Issue > Full Record

THE ALMOST SURE CONVERGENCE OF AANA SEQUENCES IN DOUBLE ARRAYS

Journal title : Bulletin of the Korean Mathematical Society
Volume 43, Issue 1, 2006, pp.169-178
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2006.43.1.169

Title & Authors

THE ALMOST SURE CONVERGENCE OF AANA SEQUENCES IN DOUBLE ARRAYS
Ko Mi-Hwa; Ryu Dae-Hee; Kim Tae-Sung;

Abstract

For double arrays of constants ${${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$}$ and sequences ${${X_n,\;n{\geq}1}$}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of ${$\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$}$ is derived.

Keywords

almost sure convergence;double arrays;asymptotically almost negatively associated;weighted sums;

Language

English

Cited by

References

R. C. Bradley, W. Bryc, and S. Janson, On dominations between measures of dependence, J. Multivariate Anal. 23 (1987), no. 2, 312-329

T. K. Chandra and S. Ghosal, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar. 71 (1996), no. 4, 327-336

T. K. Chandra and S. Ghosal, The strong law of large numbers for weighted averages under dependence assumptions, J. Theoret. Probab. 9 (1996), no. 3, 797-809

B. D. Choi and S. H. Sung, Almost sure convergence theorem of weighted sums of random variables, Stochastic Anal. Appl. 5 (1987), no. 4, 365-377

K. Joag-Dev and F. Proschan, Negative association of random variables, with application, Ann. Statist. 11 (1983), no. 1, 286-295

T. S. Kim and M. H. Ko, On the strong law for asymptotically almost negatively associated random variables, Rocky Mountain J. Math. 34 (2004), no. 3, 979-989

P. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 (1992), no. 3, 209-213