A Weak Convergence of the Linear Random Field Generated by Associated Randomvariables ℤ2

The Limiting Behaviors of Linear Random Fields Generated by Lnqd Random Variables on Z2

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on Z.

The Weak Convergence for Functions of Negatively Associated Random Variables

Weak Convergence of Random Functions

Let {vij}, i, j = 1, 2, . . . , be i.i.d. symmetric random variables with E(v 11) < ∞, and for each n let Mn = 1 sVnV T n , where Vn = (vij), i = 1, 2, . . . , n, j = 1, 2, . . . , s = s(n), and n/s → y > 0 as n → ∞. Denote by OnΛnO n the spectral decomposition of Mn. Define X ∈ D[0, 1] by Xn(t) = √ n 2 ∑[nt] i=1(y 2 i − 1 n), where (y1, y2, . . . , yn) = O (± 1 √ n ,± 1 √ n , . . . ,± 1 √ n ) ...

Weak Convergence of Random Sets

In this paper the classical Portmanteau theorem which provides equivalent conditions of weak convergence of sequence of probability measures is extended on the space of the sequence of probability measures induced by random sets.

The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables

In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...