General Central Limit Theorems for Associated Sequences

Abstract

In this paper, we provide general central limit theorems (CLT's) for associated random variables (rv's) following the approaches used by Newman (1980) and Olivera et al.(2012). Given some assumptions, a Lyapounov-Feller-Levy type theorem is stated. We next specify different particular CLT versions of associated sequences based on moment conditions. A comparison study with available CTL's is performed. As a by-product, we complete an important available theorem where an assumption was missing.