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THE WEAK LAWS OF LARGE NUMBERS FOR SUMS OF ASYMPTOTICALLY ALMOST NEGATIVELY ASSOCIATED RANDOM VECTORS IN HILBERT SPACES

  • Received : 2019.06.24
  • Accepted : 2019.08.06
  • Published : 2019.08.15

Abstract

In this paper, the weak laws of large numbers for sums of asymptotically almost negatively associated random vectors in Hilbert spaces are investigated. Some results in Hien and Thanh ([3]) are generalized to asymptotically almost negatively random vectors in Hilbert space.

Acknowledgement

Supported by : Sehan University

References

  1. T. K. Chandra and S. Ghosal, Extensions of strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Act. Math. Hung., 71 (1996), 327-336.
  2. T. K. Chandra and S. Ghosal, The strong law of large numbers for weighted averages under dependence assumptions, J. Theor. Probab., 9 (1996), 797-809.
  3. N. T. T. Hien and L. V. Thanh, On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces, Statist. Probab. Letts., 107 (2015), 236-245.
  4. N. V. Huan, N. V. Quang, and N. T. Thuan, Baum-Katz type theorems for coordinatewise negatively associated random vectors in Hilbert spaces, Acta Math. Hungar., 144 (2014), 132-149.
  5. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 11 (1983), 286-295.
  6. M. H. Ko, T. S. Kim, and K. H. Han, A note on the almost sure convergence for dependent random variables in a Hilbert space, J. Theoret. Probab., 22 (2009), 506-513.
  7. M. H. Ko, T. S. Kim, and Z. Y. Lin, The Hajeck-Renyi inequality for the AANA random variables and its applications, Taiwan J. Math., 9 (2005), no. 1, 111-122. https://doi.org/10.11650/twjm/1500407749
  8. A. T. Shen and R. C. Wu, Strong convergence for sequences of asymptotically almost negatively associated random variables, Stochastics, 86 (2014), no. 2, 291-303. https://doi.org/10.1080/17442508.2013.775289
  9. X. F. Tang, (2013) Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables, J. Inequal. Appl., (2013), no. 4, 11 pages.
  10. X. J.Wang, S. H. Hu, andW. Z. Yang, Convergence properties for asymptotically almost negatively associated sequence, Disc. Dyna. Nat. Soc., Article ID 21830 (2010), 15 pages.
  11. D. M. Yuan and J. An, Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications, Science China Ser. A: Mathematics, 52 (2009), 1887-1904.
  12. D. M. Yuan and J. An, Laws of large numbers for Cesaro alpha-integrable random variables under dependence condition AANA or AQSI, Sinica. Engl. Ser., 28 (2012), no. 6, 1103-1118.
  13. D. M. Yuan and X. S. Wu, Limiting behaviors of the maximum of the partial sum for asymptotically negatively associated random variables under residual Cesaro alpha-integrability assumption, J. Statistical Plan. Infer., 140 (2010), 2395-2402.
  14. L. X. Zhang, Strassen's law of the iterated logarithm for negatively associated random vectors, Stoch. Process Appl., 95 (2001), 311-328.