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Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables

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Abstract

In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund’s strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro’s and Riesz’s sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409–412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105–112, 2000), Li et al. (J. Theor. Probab. 8, 49–76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169–178, 1993) are also improved and extended to the negatively associated setting.

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Correspondence to Han-Ying Liang.

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Jing, BY., Liang, HY. Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables. J Theor Probab 21, 890–909 (2008). https://doi.org/10.1007/s10959-007-0128-4

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  • DOI: https://doi.org/10.1007/s10959-007-0128-4

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