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Exponential inequalities for N-demimartingales and negatively associated random variables

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  • Christofides, Tasos C.
  • Hadjikyriakou, Milto

Abstract

The class of N-demimartingales generalizes in a natural way the concept of negative association and includes as special cases martingales with respect to the natural choice of [sigma]-algebras. For this class of random variables, a number of maximal and other inequalities were obtained by [Christofides, T.C., 2003. Maximal inequalities for N-demimartingales. Archives of Inequalities and Applications 50, 397-408] and [Prakasa Rao, B.L.S., 2004. On some inequalities for N-demimartingales. J. Indian Soc. Agricultural Statist. 57, 208-216; Prakasa Rao, B.L.S., 2007. On some maximal inequalities for demisubmartingales and N-demisupermartingales. J. Inequal. Pure Appl. Math. 8, 17]. In this paper we prove Azuma's inequality for N-demimartingales and as a corollary we obtain an exponential inequality for negatively associated random variables.

Suggested Citation

  • Christofides, Tasos C. & Hadjikyriakou, Milto, 2009. "Exponential inequalities for N-demimartingales and negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2060-2065, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:2060-2065
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    Cited by:

    1. Wang, Xinghui & Wang, Xuejun, 2013. "Some inequalities for conditional demimartingales and conditional N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 700-709.
    2. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    3. Wang, Xuejun & Hu, Shuhe & Prakasa Rao, B.L.S. & Yang, Wenzhi, 2011. "Maximal inequalities for N-demimartingale and strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1348-1353, September.
    4. Hu, Shuhe & Wang, Xinghui & Yang, Wenzhi & Wang, Xuejun, 2012. "Some inequalities for demimartingales and N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 232-239.
    5. Hadjikyriakou, Milto, 2011. "Marcinkiewicz-Zygmund inequality for nonnegative N-demimartingales and related results," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 678-684, June.

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