Journal of Applied Mathematics

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

Qunying Wu

Full-text: Open access

Abstract

The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 104390, 10 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495203

Digital Object Identifier
doi:10.1155/2012/104390

Mathematical Reviews number (MathSciNet)
MR2948134

Zentralblatt MATH identifier
1253.60046

Citation

Wu, Qunying. Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables. J. Appl. Math. 2012 (2012), Article ID 104390, 10 pages. doi:10.1155/2012/104390. https://projecteuclid.org/euclid.jam/1355495203


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