Complete convergence for weighted sums of \(\rho \ast \)-mixing random variables
Summary: We obtain the complete convergence for weighted sums of \(\rho ^{\ast }\)-mixing random variables. Our result extends the result of \textit{M. Peligrad} and \textit{A. Gut} [J. Theor. Probab. 12, No.~1, 87--104 (1999; Zbl 0928.60025)] on unweighted average to a weighted average under a mild condition of weights. Our result also generalizes and sharpens the result of \textit{J. An} and \textit{D. Yuan} [Stat. Probab. Lett. 78, No.~12, 1466--1472 (2008; Zbl 1155.60316)].
scientific article; zbMATH DE number 5701489