About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 562838, 8 pages
http://dx.doi.org/10.1155/2012/562838
Research Article

Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

1School of Mathematics and Computational Science, Anqing Teachers College, Anqing 246133, China
2College of Water Conservancy and Hydropower Engineering, HoHai University, Nanjing 210098, China
3College of Mathematics and Computation Science, Anhui Normal University, Wuhu 241000, China

Received 22 June 2012; Accepted 10 September 2012

Academic Editor: Garyfalos Papaschinopoulos

Copyright © 2012 Xueping Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. W. Block, T. H. Savits, and M. Shaked, “Some concepts of negative dependence,” The Annals of Probability, vol. 10, no. 3, pp. 765–772, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. D. Yuan and J. An, “Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications,” Science in China A, vol. 52, no. 9, pp. 1887–1904, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. X. Wang, S. Hu, and W. Yang, “Convergence properties for asymptotically almost negatively associated sequence,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 218380, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. X. Wang, S. Hu, and W. Yang, “Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 717126, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. 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. View at Zentralblatt MATH
  10. J. Baek II, “Almost sure convergence for asymptotically almost negatively associated random variables sequence,” Communications of the Korean Statistical Society, vol. 16, no. 6, pp. 1013–1022, 2009. View at Publisher · View at Google Scholar
  11. Q. Y. Wu, “Probability limit theory for mixing sequence,” Sciences Press, 2005 (Chinese).
  12. S. H. Sung, “Strong laws for weighted sums of i.i.d. random variables. II,” Bulletin of the Korean Mathematical Society, vol. 39, no. 4, pp. 607–615, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH