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Some strong limit theorems for weighted product sums of \(\widetilde{\rho}\)-mixing sequences of random variables. (English) Zbl 1190.60023

Summary: We study almost sure convergence for \(\widetilde{\rho}\)-mixing sequences of random variables. Many of the previous results are our special cases. For example, the authors extend and improve the corresponding results of X. Chen, L.-X. Zhu and K.-T. Fang [Stat. Sin. 6, No. 2, 499–507 (1996; Zbl 0842.62010)] and the authors [Stat. Probab. Lett. 78, No. 8, 1017–1023 (2008; Zbl 1148.60020)]. We extend the classical Jamison convergence theorem and the Marcinkiewicz strong law of large numbers for independent sequences of random variables to \(\widetilde{\rho}\)-mixing sequences of random variables without necessarily adding any extra conditions.

MSC:

60F15 Strong limit theorems
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References:

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