Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of ρ

The equivalent conditions of complete convergence are established for weighted sums of ρ~-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 ρ~-mixing random variables is obtained

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

The equivalent conditions of complete convergence are established for weighted sums of̃-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 of̃-mixing random variables is obtained