##
**Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables.**
*(English)*
Zbl 1235.60026

Summary: Let \(\{X_{ni}, i \geq 1, n \geq 1\}\) be an array of rowwise asymptotically almost negatively associated random variables. Sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.

### MSC:

60F15 | Strong limit theorems |

### Keywords:

complete convergence; Marcinkiewicz-Zygmund type strong law of large numbers; asymptotically almost negatively associated random variables
PDFBibTeX
XMLCite

\textit{X. Wang} et al., Discrete Dyn. Nat. Soc. 2011, Article ID 717126, 11 p. (2011; Zbl 1235.60026)

Full Text:
DOI

### References:

[1] | P. L. Hsu and H. Robbins, “Complete convergence and the law of large numbers,” Proceedings of the National Academy of Sciences of the United States of America, vol. 33, pp. 25-31, 1947. · Zbl 0030.20101 |

[2] | K. Joag-Dev and F. Proschan, “Negative association of random variables, with applications,” The Annals of Statistics, vol. 11, no. 1, pp. 286-295, 1983. · Zbl 0508.62041 |

[3] | P. Matuła, “A note on the almost sure convergence of sums of negatively dependent random variables,” Statistics & Probability Letters, vol. 15, no. 3, pp. 209-213, 1992. · Zbl 0925.60024 |

[4] | T. K. Chandra and S. Ghosal, “Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables,” Acta Mathematica Hungarica, vol. 71, no. 4, pp. 327-336, 1996. · Zbl 0853.60032 |

[5] | T. K. Chandra and S. Ghosal, “The strong law of large numbers for weighted averages under dependence assumptions,” Journal of Theoretical Probability, vol. 9, no. 3, pp. 797-809, 1996. · Zbl 0857.60021 |

[6] | M.-H. Ko, T.-S. Kim, and Z. Lin, “The Hájeck-Rènyi inequality for the AANA random variables and its applications,” Taiwanese Journal of Mathematics, vol. 9, no. 1, pp. 111-122, 2005. · Zbl 1069.60022 |

[7] | Y. Wang, J. Yan, F. Cheng, and C. Su, “The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables,” Southeast Asian Bulletin of Mathematics, vol. 27, no. 2, pp. 369-384, 2003. · Zbl 1061.60031 |

[8] | D. Yuan and J. An, “Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications,” Science in China. Series A: Mathematics, vol. 52, no. 9, pp. 1887-1904, 2009. · Zbl 1184.62099 |

[9] | X. J. Wang, S. H. Hu, and W. Z. Yang, “Convergence properties for asymptotically almost negatively associated sequence,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 218380, 15 pages, 2010. · Zbl 1207.60025 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.