Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of ρ~-Mixing Random Variables

Abstract

The equivalent conditions of complete convergence are established for weighted sums of $\tilde{\rho }$-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 $\tilde{\rho }$-mixing random variables is obtained.