Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 630608, 13 pages
doi:10.1155/2010/630608
Research Article

Complete Convergence for Weighted Sums of ρ∗-Mixing Random Variables

Soo Hak Sung

Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South Korea

Received 2 August 2009; Accepted 24 March 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 Soo Hak Sung. 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 obtain the complete convergence for weighted sums of ρ∗-mixing random variables. Our result extends the result of Peligrad and Gut (1999) on unweighted average to a weighted average under a mild condition of weights. Our result also generalizes and sharpens the result of An and Yuan (2008).