Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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HÀJECK-RÈNYI TYPE INEQUALITY AND STRONG LAW OF LARGE NUMBERS FOR AQSI RANDOM VARIABLES

  • Ryu, Dae-Hee (Department of Computer Science ChungWoon University)
  • Received : 2010.10.14
  • Accepted : 2010.11.24
  • Published : 2010.12.30
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Abstract

In this paper we study the $H{\grave{a}}jeck-R{\grave{e}}nyi$ type inequality and strong law of large numbers for asymptotically quadrant sub-independent(AQSI) sequences. We also prove the integrability of supremum for AQSI sequences.

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References

  1. T. Birkel, Laws of large numbers under dependence assumptions, Statist Probab Letts. 14 (1992), 355-362. https://doi.org/10.1016/0167-7152(92)90096-N
  2. T. K. Chandra and S. Ghosal, Some elementary strong laws of large numbers: a Riew, Tech. Report,(1993) Indian Statistical Institute.
  3. 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), 237-259.
  4. J. Esary, F. Proschan, and D. Walkup, Association of random variables with applications, Ann. Math. Statist. 38 (1967), 1466-1474. https://doi.org/10.1214/aoms/1177698701
  5. I. Fazekas and O. Klesov, A geneal approach to the strong laws of large numbers, Theory of Probability and its applications 45 (2000), 436-449.
  6. J.Hajeck, and A.Renyi, A generalization of an inequality of Kolmogorov, Acta Math. Acad. Sci. Hungar 6 (1955), 281-284. https://doi.org/10.1007/BF02024392
  7. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295. https://doi.org/10.1214/aos/1176346079
  8. M. H. Ko, T. S. Kim, and Z. Lin, The Hµajeck-Rµenyi inequality for the AANA random variables and its applications, Taiwanese J. Math. 9 (2005), 111-122. https://doi.org/10.11650/twjm/1500407749
  9. E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260
  10. J. Liu, S. Gan, and P. Chen, The Hajeck-Renyi inequality for the NA random variables and its application, Statist. Probab. Lett. 43 (1999), 99-105. https://doi.org/10.1016/S0167-7152(98)00251-X
  11. B. L. S. Prakasa Rao, Hµajeck-Rµenyi type inequality for associated sequences, Statist. Probab. Lett. 57 (2002), 139-143. https://doi.org/10.1016/S0167-7152(02)00025-1
  12. H. Shuhe and X. Wang, W. Yang, The Hµajeck-Rµenyi type inequality for asso- ciated random variables, Stat. Probab. Lett. 79 (2009), 884-888. https://doi.org/10.1016/j.spl.2008.11.014
  13. S. H. Sung, A note on the Hajeck-Renyi inequality for associated random variables, Stat. Probab. Lett. 78 (2008), 885-889. https://doi.org/10.1016/j.spl.2007.09.015