Strong Laws of Large Numbers for Arrays of Rowwise NA and LNQD Random Variables

Jiangfeng Wang,Qunying Wu

doi:10.1155/2011/708087

Abstract

Some strong laws of large numbers and strong convergence properties for arrays of rowwise negatively associated and linearly negative quadrant dependent random variables are obtained. The results obtained not only generalize the result of Hu and Taylor to negatively associated and linearly negative quadrant dependent random variables, but also improve it.

Highlights

Let {Xn}n∈N be a sequence of independent distributed random variables
The aim of this paper is to establish a strong law of large numbers for arrays of NA and LNQD random variables
Let {Xn, n ≥ 1} be LNQD random variables sequences with mean zero and 0 < Bn n k

Summary

Introduction

Let {Xn}n∈N be a sequence of independent distributed random variables. The MarcinkiewiczZygmund strong law of large numbers SLLN provides that 1n n1/α i 1 Xi − EXi−→ 0 a.s. for 1 ≤ α < 2, 1 n1/α n Xi i1 −→a.s. for 0 < α < 1 as n −→ ∞if and only if E|X|α < ∞. Let {Xni, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of rowwise independent random variables. A sequence {Xn}n∈N of random variables is said to be pairwise NQD if Xi and Xj are NQD for all i, j ∈ N and i / j.

Objectives

Results

Conclusion