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Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables. (English) Zbl 1253.60046
Summary: The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far, no general moment inequality for PNQD sequences has been given, and therefore the study of the limit theory for PNQD sequences is very difficult and challenging. We establish a collection that contains a relationship to overcome the difficulty 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 L. E. Baum and M. Katz [Trans. Am. Math. Soc. 120, 108–123 (1965; Zbl 0142.14802)] and Q. Wu and Y. Wang [J. Syst. Sci. Math. Sci. 22, No. 2, 192–199 (2002; Zbl 1038.60020)].

60F15Strong limit theorems