Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T03:57:59.787Z Has data issue: false hasContentIssue false

On strong convergence of arrays

Published online by Cambridge University Press:  17 April 2009

Yong-Cheng Qi
Affiliation:
Institute of Systems Science Academia SinicaBeijing 100080 People'sRepublic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study almost sure convergence for arrays of independent and identically distributed random variables. We obtain a condition under which Marcinkiewicz's strong law holds and get a rate analogous to the law of the iterated logarithm under a condition weaker than Hu and Weber's.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[l] Baum, L.E. and Katz, M., ‘Convergence rates in the law of large numbers’, Trans. Amer.Math. Soc. 120 (1965), 108123.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. Hungar. 54 (1989), 153162.Google Scholar
[3]Hu, T.C. and Weber, N.C., ‘On the rate of convergence in the strong law of large numbers for arrays’, Bull. Austral. Math. Soc. 45 (1992), 479482.Google Scholar
[4]Rogozin, B.A., ‘On the existence of exact upper sequences’, Theory Probab. Appl. 13 (1968), 667671.Google Scholar
[5]Rubin, H. and Sethuraman, J., ‘Probabilities of moderate deviationsSankhyā Ser. A 27(1965), 325346.Google Scholar