Rocky Mountain Journal of Mathematics

On the Strong Law for Asymptotically Almost Negatively Associated Random Variables

Tae-Sung Kim, Mi-Hwa Ko, and Il-Hyun Lee

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Rocky Mountain J. Math., Volume 34, Number 3 (2004), 979-989.

First available in Project Euclid: 5 June 2007

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Zentralblatt MATH identifier

Primary: 60F15: Strong theorems

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


Kim, Tae-Sung; Ko, Mi-Hwa; Lee, Il-Hyun. On the Strong Law for Asymptotically Almost Negatively Associated Random Variables. Rocky Mountain J. Math. 34 (2004), no. 3, 979--989. doi:10.1216/rmjm/1181069838.

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  • R.C. Bradley, W. Bryc and S. Janson, On dominations between measures of dependence, J. Multivariate Anal. 3 (1987), 312-329.
  • 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), 327-336.
  • --------, The strong law of large numbers for weighted averages under dependence assumption, J. Theoret. Probab. 9 (1996), 797-809.
  • Y.S. Chow, A martingale inequality and the law of large numbers, Proc. Amer. Math. Soc. 11 (1960), 107-111.
  • T.C. Christofides, Maximal inequalities for demimartingales and a strong law of large number, Statist. Probab. Lett. 50 (2000), 357-363.
  • S. Gan, The Hajeck-Renyi inequality for Banach space valued martingales and the $p$ smoothness of Banach space, Statist. Probab. Lett. 32 (1997), 245-248.
  • J. Hajeck and A. Renyi, Generalization of an inequality of Kolmogorov, Acta Math. Acad. Sci. Hungar. 6 (1955), 281-283.
  • K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295.
  • 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.
  • P. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 (1992), 209-213.