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Complete moment convergence for weighted sums of negatively orthant dependent random variables

Wang Xuejun (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Chen Zhiyong (Xiamen University, School of Mathematical Sciences, Xiamen, P.R. China)
Xiao Ru (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Xie Xiujuan (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

Keywords: negatively orthant dependent random variables, complete convergence, complete moment convergence, weighted sums