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COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES

Published online by Cambridge University Press:  01 September 2008

GUANG-HUI CAI  and
BAO-CAI GUO
GUANG-HUI CAI
Affiliation:
Department of Mathematics and Statistics, Zhejiang Gongshang University, Hangzhou 310035, P. R. China e-mail: [email protected]
BAO-CAI GUO
Affiliation:
Department of Mathematics and Statistics, Zhejiang Gongshang University, Hangzhou 310035, P. R. China e-mail: [email protected]
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Abstract

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Let Xn, n ≥ 1 be an asymptotically almost negatively associated (AANA) sequence of random variables. Some complete convergence and Marcinkiewicz–Zygmund type strong laws of large numbers for an AANA sequence of random variables are obtained. The results obtained generalize the results of Kim, Ko and Lee (Kim, T. S., Ko, M. H. and Lee, I. H. 2004. On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. of Math. 34, 979–989.).

Keywords

60F15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 351 - 357
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Baum, L. E. and Katz, M., Convergence rates in the law of large numbers, Trans. Amer. Math. Soc. 120 (1965), 108–123.CrossRefGoogle Scholar
2.Chandra, T. K. and Ghosal, S., Extensions of the strong laws of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar. 32 (1996a), 327–336.CrossRefGoogle Scholar
3.Chandra, T. K. and Ghosal, S., The strong laws of large numbers for weighted averages under dependence assumptions, J. Theor. Probab. 9 (1996b), 797–809.Google Scholar
4.Chow, Y. S. and Lai, T. L., Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossings, Trans. Amer. Math. Soc. 208 (1975), 51–72.CrossRefGoogle Scholar
5.Chow, Y. S. and Lai, T. L., Paley-type inequalities and convergence rates related to the law of large numbers and extended renewal theory, Z. Wahrsch. Verw. Geb. 45 (1978) 1–19.CrossRefGoogle Scholar
6.Erdös, P., On a theorem of Hsu–Robbins, Ann. Math. Statist. 20 (1949), 286–291.Google Scholar
7.Hsu, P. L. and Robbins, H., Complete convergence and the law of larege numbers, Proc. Nat. Acad. Sci. (USA) 33 (2) (1947), 25–31.Google Scholar
8.Kim, T. S., Ko, M. H. and Lee, I. H., On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. Math. 34 (224), 979–989.Google Scholar
9.Petrov, V. V., Limit theorems of probability theory sequences of independent random variables (Oxford, Oxford Science Publications, 1995).Google Scholar