Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 107096, 14 pages
http://dx.doi.org/10.5402/2012/107096
Research Article

Weak and Almost Sure Convergence for Products of Sums of Associated Random Variables

Institute of Mathematics, Marie Curie-Skłodowska University, PL. M. C.-Skłodowskiej 1, 20-031 Lublin, Poland

Received 23 March 2012; Accepted 12 April 2012

Academic Editors: P. Burman, S. Lototsky, and H. J. Paarsch

Copyright © 2012 Przemysław Matuła and Iwona Stępień. 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

We study weak convergence of product of sums of stationary sequences of associated random variables to the log-normal law. The almost sure version of this result is also presented. The obtained theorems extend and generalize some of the results known so far for independent or associated random variables.