Journal of Applied Mathematics
Volume 2013 (2013), Article ID 656257, 9 pages
http://dx.doi.org/10.1155/2013/656257
Research Article

The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences

Yuanying Jiang1,2 and Qunying Wu1

1College of Science, Guilin University of Technology, Guilin 541004, China
2School of Statistics, Renmin University of China, Beijing 100872, China

Received 13 May 2013; Accepted 18 June 2013

Academic Editor: Ying Hu

Copyright © 2013 Yuanying Jiang and Qunying Wu. 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

In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables: , almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central limit theorems from the i.i.d. case to the stationary negatively associated sequences.