A central limit theorem for weighted sums of associated random field

ABSTRACT

In this paper we obtain the central limit theorem for weighted sums of the form ∑_{1 ⩽ i ⩽ n}a_{n, i}X_i, where is an array of non negative numbers such that , max _{1 ⩽ i ⩽ n}a_{n, i} → 0 as n → ∞ and is a field of associated random variables with EX_i = 0 and EX²_i < ∞. As application, we give a central limit theorem for the partial sum of linear random field .

Keywords:

• Associated
• Central limit theorem
• Random field
• Uniformly integrable
• Weighted sums

Mathematics Subject Classification:

• 60F05