Limit theorems for dependent random variables

Convergence Properties of the Partial Sums for Sequences of End Random Variables

“…Joag-Dev and Proschan ( [6]) once pointed out that NA (negatively associated) implies ND, but neither NUD nor NLD implies NA. Since the paper of Joag-Dev and Proschan ( [6]) appeared, the convergence properties of ND random sequences have been studied by Bozorgnia and Patterson ( [2]), Taylor et al ([13], [14]), Amini and Bozorgnia ([1]), Mi-Hwa Ko et al ( [7], [8]). …”

Strong Limit Theorems for Weighted Sums of Nod Sequence and Exponential Inequalities

“…The main results of this paper are depending on the following lemmas: Lemma 1.1 (cf. Bozorgnia, et al, [3]). Let random variables X 1 , X 2 , .…”

A Strong Law of Large Numbers for Set-Valued Negatively Dependent Random Variables

“…Lemma 2.1 (Bozorgnia, Patterson & Taylor, 1993) Let real-valued random variables {x i : 1 ≤ i ≤ n} be negatively dependent. Then the following are true:…”

“…For more contents about negatively dependent random variables, readers can refer to (Bozorgnia, Patterson & Taylor, 1992), (Bozorgnia, Patterson & Taylor, 1993), (Bozorgnia, Patterson & Taylor, 1997), (Taylor & Patterson, 1997).…”

“…Negative dependence has been particularly useful in obtaining strong laws of large numbers. Bozorgnia, Patterson and Taylor discussed the properties for negatively dependent random variables in (Bozorgnia, Patterson & Taylor, 1993), and proved the laws of large number for negative dependence random variables in (Bozorgnia, Patterson & Taylor, 1992). The limit theorems of single-valued negative dependence random variables have been extensively studied and got very interesting results (Mi & Tae, 2005) (Valentin, 1995), but all the results are limited to single-valued random variables.…”