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Limit theorems for triangular arrays under a relaxed asymptotic negligibility condition

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

Miloslav Jirina
Miloslav Jirina
Affiliation:
School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, S. A. 5042, Australia
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Abstract

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Let {Xnk} be a triangular array of independent random variables satisfying the so-called tail-negligibility condition, i.e. such that Prob{|Xnk| > a} → 0 as both k, n → ∞. It is also assumed that for each fixed k, Xnk converges in distribution as n → ∞. Theorems on the asymptotic behavior of the row sums of the array, analogous to those of the classical theory under the uniform negligibility condition, are presented.

Keywords

triangular array of independent random variableslimit theorems for sumstail negligibility

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 1 , February 1987 , pp. 117 - 128
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Feller, W., An Introduction to Probability Theory and Its Applications, Vol. II (2nd ed., Wiley, New York, 1971).Google Scholar
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[3]Zolotarev, V. M., ‘A generalization of the Lindeberg-Feller theorem,’ Theory Probab. Appl. 12 (1967), 608–618.CrossRefGoogle Scholar