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A REMARK ON THE STRONG LAW FOR B-VALUED ARRAYS OF RANDOM ELEMENTS

Part of: Limit theorems

Published online by Cambridge University Press:  02 June 2010

TIEN-CHUNG HU ,
PING YAN CHEN  and
N. C. WEBER
TIEN-CHUNG HU
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan (email: tchu@math.nthu.edu.tw)
PING YAN CHEN
Affiliation:
Department of Mathematics, Jinan University, Guangzhou, 510630, PR China (email: tchenpy@jnu.edu.cn)
N. C. WEBER*
Affiliation:
School of Mathematics and Statistics, University of Sydney, Australia (email: neville.weber@sydney.edu.au)
*
✉For correspondence; e-mail: neville.weber@sydney.edu.au
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Abstract

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The conditions in the strong law of large numbers given by Li et al. [‘A strong law for B-valued arrays’, Proc. Amer. Math. Soc.123 (1995), 3205–3212] for B-valued arrays are relaxed. Further, the compact logarithm rate law and the bounded logarithm rate law are discussed for the moving average process based on an array of random elements.

Keywords

law of the iterated logarithmBanach spacealmost sure limitmoving average process

MSC classification

Secondary: 60F15: Strong theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 31 - 43
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Einmahl, U. and Li, D. L., ‘Characterization of the LIL behavior in Banach space’, Trans. Amer. Math. Soc. 360 (2008), 6677–6693.CrossRefGoogle Scholar
[2]Hartman, P. and Wintner, P., ‘On the law of the iterated logarithm’, Amer. J. Math. 63 (1941), 169–176.CrossRefGoogle Scholar
[3]Hu, T.-C. and Weber, N. C., ‘On the rate of convergence in the strong law of large numbers for arrays’, Bull. Aust. Math. Soc. 45 (1992), 279–282.CrossRefGoogle Scholar
[4]Ledoux, M. and Talagrand, M., Probability in Banach Spaces (Springer, Berlin, 1991).CrossRefGoogle Scholar
[5]Li, D. L. and Huang, M. L., ‘Strong invariance principles for arrays’, Bull. Inst. Math. Acad. Sin. 28 (2000), 167–181.Google Scholar
[6]Li, D. L., Rao, M. B. and Tomkins, K. J., ‘A strong law for B-valued arrays’, Proc. Amer. Math. Soc. 123 (1995), 3205–3212.Google Scholar
[7]Qi, Y. C., ‘On the strong convergence of arrays’, Bull. Aust. Math. Soc. 50 (1994), 219–223.CrossRefGoogle Scholar
[8]Strassen, V., ‘A converse to the law of the iterated logarithm’, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 4 (1960), 265–268.CrossRefGoogle Scholar