Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-12T11:58:08.596Z Has data issue: false hasContentIssue false
  • English
  • Français

An analogue of Kolmogorov's law of the iterated logarithm for arrays

Published online by Cambridge University Press:  17 April 2009

Soo Hak Sung
Soo Hak Sung
Affiliation:
Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South Korea e-mail: [email protected]
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.

This paper is concerned with the almost sure convergence for arrays of independent, but not necessarily identically distributed, random variables. We show that Kolmogorov's law of the iterated logarithm does not hold for arrays and obtain an analogue of Kolmogorov's law.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 177 - 182
Copyright
Copyright © Australian Mathematical Society 1996

References

REFERENCES

[1]Hu, T.C., ‘On the law of the iterated logarithm for arrays of random variables’, Comm. Statist. Theory Methods 20 (1991), 1989–1994.CrossRefGoogle Scholar
[2]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), 479–482.CrossRefGoogle Scholar
[3]Qi, Y.C., ‘On strong convergence of arrays’, Bull. Austral. Math. Soc. 50 (1994), 219–223.CrossRefGoogle Scholar
[4]Rosalsky, A., ‘On the number of successes in independent trials’, Sankhyā Ser. A 47 (1985), 380–391.Google Scholar
[5]Stout, W.F., Almost sure convergence (Academic Press, New York, 1974).Google Scholar
[6]Teicher, H., ‘Almost certain behavior of row sums of double arrays’, Lecture Notes in Mathematics 861 (Springer-Verlag, Berlin, Heidelberg, New York, 1981), pp. 155–165.Google Scholar