Exponential inequalities for N-demimartingales and negatively associated random variables

Tasos C. Christofides and Milto Hadjikyriakou

Statistics & Probability Letters, 2009, vol. 79, issue 19, 2060-2065

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.

Date: 2009
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