On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean

Journal of Theoretical Probability - In this work, we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions....     

Exponential inequalities for N-demimartingales and negatively associated random variables

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 σ-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.