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

Abstract EN

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.