Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

  • Xuejun, Wang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
  • Shuhe, Hu (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
  • Xiaoqin, Li (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
  • Wenzhi, Yang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
  • Received : 2009.09.27
  • Published : 2011.01.31
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Abstract

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

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References

  1. T. K. Chandra and S. Ghosal, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar. 71 (1996), no. 4, 327-336. https://doi.org/10.1007/BF00114421
  2. T. K. Chandra and S. Ghosal, The strong law of large numbers for weighted averages under dependence assumptions, J. Theoret. Probab. 9 (1996), no. 3, 797-809. https://doi.org/10.1007/BF02214087
  3. I. Fazekas and O. Klesov, A general approach to the strong laws of large numbers, Teor. Veroyatnost. i Primenen. 45 (2000), no. 3, 568-583; translation in Theory Probab. Appl. 45 (2002), no. 3, 436-449. https://doi.org/10.4213/tvp486
  4. M. H. Ko, T. S. Kim, and Z. Y. Lin, The Hajeck-Renyi inequality for the AANA random variables and its applications, Taiwanese J. Math. 9 (2005), no. 1, 111-122. https://doi.org/10.11650/twjm/1500407749
  5. Y. B. Wang, J. G. Yan, and F. Y. Cheng, The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables, Southeast Asian Bull. Math. 27 (2003), no. 2, 369-384.
  6. D. M. Yuan and J. An, Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications, Sci. China Ser. A 52 (2009), no. 9, 1887-1904. https://doi.org/10.1007/s11425-009-0154-z

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  2. Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables vol.2013, 2013, https://doi.org/10.1155/2013/741901
  3. Maximal inequalities and strong law of large numbers for sequences of m-asymptotically almost negatively associated random variables vol.46, pp.6, 2017, https://doi.org/10.1080/03610926.2015.1048885
  4. Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables vol.109, pp.1, 2015, https://doi.org/10.1007/s13398-014-0174-6
  5. Strong Convergence Properties and Strong Stability for Weighted Sums of AANA Random Variables vol.2013, 2013, https://doi.org/10.1155/2013/295041
  6. Lr convergence for arrays of rowwise asymptotically almost negatively associated random variables 2017, https://doi.org/10.1080/03610926.2017.1285932
  7. Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-4