Limiting behaviour for arrays of row-wise END random variables under conditions of h-integrability

Abstract

The authors study Lr-convergence, complete convergence and complete moment convergence for arrays of row-wise extended negatively dependent random variables under some appropriate conditions of h-integrability. The results in this paper extend and improve the results of Sung et al. [H.S. Sung, S. Lisawadi, A. Volodin, Weak laws of large numbers for arrays under a condition of uniform integrability, J. Korean Math. Soc. 45 (2008), pp. 289–300].