The equivalent conditions of complete convergence are established for weighted sums of -mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence of -mixing random variables is obtained.
"Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of -Mixing Random Variables." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/612140