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

Abstract

Negatively orthant dependence is regarded as a generalisation of independence for random variables, introduced by K. Joag-Dev and F. Proschan. Numerous researchers have investigated inequalities and laws of large numbers for such sequences of random variables. In particular, the concept of complete convergence, defjned by P. L. Hsu and H. Robbins, has attracted signifjcant attention. Complete convergence for partial weighted sums of negatively orthant dependent random variables dominated by a random variable X is established. SufÐcient conditions for this type of convergence are provided under mild assumptions on the weights and the moments of random variable X.