DOI QR코드

DOI QR Code

ON THE MAXIMAL INEQUALITY FOR AANA RANDOM VARIABLES AND A STRONG LAW OF LARGE NUMBERS

  • Kim, Tae-Sung (Division of Mathematics and Informational Statistics and Institute of Basic Natural Science Wonkwang University) ;
  • Ko, Mi-Hwa (Statistical Research Center for Complex Systems Seoul National University)
  • 발행 : 2003.07.01

초록

In this paper we Obtain the Hajeck-Renyi type inequality for the asymptotically almost negatively associated(AANA) random variables and extend some results for negatively associated random variables to the AANA case by applying this inequality.

키워드

참고문헌

  1. Acta. Math. Hungar. v.71 Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables T.K.Chandra;S.Ghosal https://doi.org/10.1007/BF00114421
  2. J. Theor. Probab. v.9 The strong law of large numbers for weighted averages under dependence assumption T.K.Chandra https://doi.org/10.1007/BF02214087
  3. Proc. Amer. Math. Soc. v.11 A martingale inequality and the law of large numbers Y.S.Chow https://doi.org/10.2307/2032726
  4. Statist. Probab. Lett. v.50 Maximal inequalities for demimartingales and a strong law of large number T.C.Christofides https://doi.org/10.1016/S0167-7152(00)00116-4
  5. Statist. Probab. Lett. v.32 The Hajeck-Renyi inequality for Banach space valued martingales and the p smoothness of Banach space S.Gan https://doi.org/10.1016/S0167-7152(96)00080-6
  6. Acta. Math. Acad. Sci. Hungar. v.6 Generalization of an inequality of Kolmogorov J.Hajeck;A.Renyi https://doi.org/10.1007/BF02024392
  7. Ann. Statist. v.11 Negative association of random variables with applications K.Joag-Dev;F.Proschan https://doi.org/10.1214/aos/1176346079
  8. Statist. Probab. Lett. v.43 The Hajeck-Renyi inequality for the NA random variables and its application J.Liu;S.Gan;P.Chen https://doi.org/10.1016/S0167-7152(98)00251-X
  9. Statist. Probab. Lett. v.15 A note on the almost sure convergence of sums of negatively dependent random variables P.Matula https://doi.org/10.1016/0167-7152(92)90191-7