On Complete Convergence for Weighted Sums of ρ * -Mixing Random Variables

Abstract

We prove the strong law of large numbers for weighted sums ${\sum }_{i=1}^n\mathrm{‍}{a}_{ni}{X}_i$, which generalizes and improves the corresponding one for independent and identically distributed random variables and $\phi$-mixing random variables. In addition, we present some results on complete convergence for weighted sums of ${\rho }^{\mathbf{*}}$-mixing random variables under some suitable conditions, which generalize the corresponding ones for independent random variables.