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On the rate of convergence in the strong law of large numbers for arrays

Published online by Cambridge University Press:  17 April 2009

Tien-Chung Hu  and
N.C. Weber
Tien-Chung Hu
Affiliation:
Department of MathematicsNational Tsing-Hua UniversityHsinchu Taiwan 30043
N.C. Weber
Affiliation:
School of Mathematics and Statistics University of SydneyNew South Wales 2006Australia
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Abstract

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For sequences of independent and identically distributed random variables it is well known that the existence of the second moment implies the law of the iterated logarithm. We show that the law of the iterated logarithm does not extend to arrays of independent and identically distributed random variables and we develop an analogous rate result for such arrays under finite fourth moments.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 479 - 482
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Hartman, P. and Wintner, A., ‘On the law of the iterated logarithm’, Amer. J. Math. 63 (1941), 169–176.CrossRefGoogle Scholar
[2]Hu, T.C., Moricz, F. and Taylor, R.L., ‘Strong laws of large numbers for arrays of rowwise independent random variables’, Acta Math. Hung. 54 (1989), 153–162.CrossRefGoogle Scholar
[3]Kolmogorov, A.N., ‘Sur la loi forte des grandes nombres’, Acad. Sci. Paris 191 (1930), 910–912.Google Scholar
[4]Michel, R., ‘Results on probabilities of moderate deviations’, Ann. Probab. 2 (1974), 349–353.CrossRefGoogle Scholar
[5]Rubin, H. and Sethuraman, J., ‘Probabilities of moderate deviations’, Sankhya A 27 (1965), 325–346.Google Scholar