On the convergence for PNQD sequences with general moment conditions

Abstract

Let {X, Xn, n ≥ 1} be a sequence of identically distributed pairwise negative quadrant dependent (PNQD) random variables and {an, n ≥ 1} be a sequence of positive constants with an = f(n) and f(θk)/f(θk−1) ≥ β for all large positive integers k, where 1 0 (x ≥ 1) is a non-decreasing function on [b, +∞) for some b ≥ 1. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X, Xn, n ≥ 1}, which are equivalent to the general moment condition $$\sum\nolimits_{n = 1}^\infty {P\left( {\left| X \right| > {a_n}} \right) < \infty }$$. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung [14].