Table of Contents
ISRN Probability and Statistics
Volume 2012 (2012), Article ID 192427, 10 pages
http://dx.doi.org/10.5402/2012/192427
Research Article

A Note on the Central Limit Theorems for Dependent Random Variables

Institute for Cyber Security, University of Texas at San Antonio, San Antonio, TX 78249, USA

Received 25 June 2012; Accepted 13 September 2012

Academic Editors: D. Fiems, A. Hutt, and M. Montero

Copyright © 2012 Yilun Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.