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Complete convergence for weighted sums of \(\rho \ast \)-mixing random variables. (English) Zbl 1193.60045

Summary: We obtain the complete convergence for weighted sums of \(\rho ^{\ast }\)-mixing random variables. Our result extends the result of M. Peligrad and 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 J. An and D. Yuan [Stat. Probab. Lett. 78, No. 12, 1466–1472 (2008; Zbl 1155.60316)].

MSC:

60F15 Strong limit theorems
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References:

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