Complete convergence for arrays of rowwise negatively orthant dependent random variables

Complete convergence for weighted sums of arrays of rowwise negatively dependent random variables

“…Some complete convergence for the maximum weighted sums of arrays of rowwise ND random variables are obtained without the assumption of identical distribution. The result generalize and improve the corresponding result of Wang et al [7].…”

“…For example, we refer to [2,4,5,6]. Recently, Wang et al [7] obtained the following complete convergence result for weighted sums of ND random variables with identical distribution. Inspired by the above theorem obtained by Wang [7], in this work, we will further study the compete convergence for weighted sums of arrays of rowwise ND random variables under some mild moment conditions, which are weaker than the above Theorem 1.1.…”

“…Recently, Wang et al [7] obtained the following complete convergence result for weighted sums of ND random variables with identical distribution. Inspired by the above theorem obtained by Wang [7], in this work, we will further study the compete convergence for weighted sums of arrays of rowwise ND random variables under some mild moment conditions, which are weaker than the above Theorem 1.1. Some complete convergence for the maximum weighted sums of arrays of rowwise ND random variables are obtained without the assumption of identical distribution.…”

Strong Convergence for weighed sums of negatively superadditive dependent random variables

“…Let {X n , n ≥ 1} be a sequence of NSD identically distributed random variables with E|X 1 | β < ∞. If β > 1, further assume that EX 1 = 0, then for any 0 < p < min(β, 2), (i) the moment condition E|X| β < ∞ in Theorem 3.1 is weaker than (2.1) in Wang et al ( [24]);…”

On the Strong Law of Large Numbers for Weighted Sums of Negatively Superadditive Dependent Random Variables

“…By the Property P 2 in Hu [4], we can see that NSD random variables are negatively orthant dependent (NOD, in short). For more details about NOD random variables, one can refer to Joag-Dev and Proschan [7] and Wang et al [16,17], Wu [21], Wu and Jiang [22], and so forth. Negatively superadditive dependent structure is an extension of negatively associated structure and sometimes more useful than it and can be used to get many important probability inequalities.…”