On the convergence for PNQD sequences with general moment conditions
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 < θ ≤ β and
f(x) > 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 ∑∞n=1 P(|X| > an) < ∞. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung[14].
关键词：
pairwise negative quadrant dependent (PNQD) random variable,
strong law of large numbers,
complete convergence,
general moment condition
