DOI QR코드

DOI QR Code

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

Kim, Tae-Sung;Ko, Mi-Hwa

  • Published : 2003.07.01

Abstract

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.

Keywords

Hajeck-Renyi inequality;negatively associated random variables;asymptotically almost negatively associated;strong law of large numbers

References

  1. 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
  2. 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
  3. Acta. Math. Acad. Sci. Hungar. v.6 Generalization of an inequality of Kolmogorov J.Hajeck;A.Renyi https://doi.org/10.1007/BF02024392
  4. 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
  5. Ann. Statist. v.11 Negative association of random variables with applications K.Joag-Dev;F.Proschan https://doi.org/10.1214/aos/1176346079
  6. 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
  7. 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
  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. Proc. Amer. Math. Soc. v.11 A martingale inequality and the law of large numbers Y.S.Chow https://doi.org/10.2307/2032726