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Complete Convergence for Weighted Sums of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>ρ</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math>-Mixing Random Variables
We obtain the complete convergence for weighted sums of ρ ∗ ‐mixing random variables. Our result extends the result of Peligrad and Gut (1999) on unweighted average to a weighted average under a mild condition of weights. Our result also generalizes and sharpens the result of An and Yuan (2008).