Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 104390, 10 pages.
Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables
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).
J. Appl. Math., Volume 2012 (2012), Article ID 104390, 10 pages.
First available in Project Euclid: 14 December 2012
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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