Stochastic Analysis and Applications

Let X1 X2 be a sequence of pairwise negatively dependent random variables with distributions F1 F2 on − , and let S n be the maximum of its first n partial sums S1 Sn. This article studies the asymptotic tail probabilities of Sn and S n . Under suitable regularity conditions on the distributions F1 Fn, we prove that both P Sn > x and P S n > x are asymptotic to ∑n i=1 1− Fi x as x → , indicating that the negative dependence among the random variables does not affect the asymptotic tail behavior of Sn and S n . For a special case where the sequence X1 X2 is generated by pairwise negatively dependent and identically distributed random variables weighted by positive constants fulfilling a certain summability condition, we further prove that the asymptotic relations obtained are uniform for all n = 1 2 .