On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

Abstract

Letan,n≥1be a sequence of positive constants withan/n↑and letX,Xn,n≥1be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition∑n=1∞PX>an<∞. Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables.

The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences

“…For pairwise negatively dependent random variables, Shen et al [43] established a strong law of large numbers for pairwise negatively dependent and identically distributed random variables under a very general condition. Precisely, Shen et al [43,Theorems 3 and 5] proved that if {b n , n ≥ 1} is a sequence of positive constants with b n /n ↑ ∞ and if {X, X n , n ≥ 1} is a sequence of pairwise negatively dependent and identically distributed random variables, then…”