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Abstract and Applied Analysis
Volume 2013, Article ID 295041, 12 pages
Research Article

Strong Convergence Properties and Strong Stability for Weighted Sums of AANA Random Variables

School of Mathematical Science, Anhui University, Hefei 230601, China

Received 10 August 2013; Accepted 22 October 2013

Academic Editor: Jaume Giné

Copyright © 2013 Zhiyong Chen et al. 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.


The Khintchine-Kolmogorov-type convergence theorem and three-series theorem for AANA random variables are established. By using these convergence theorems, we obtain convergence results for AANA sequences, which extend the corresponding ones for independent sequences and NA sequences. In addition, we study the strong stability for weighted sums of AANA random variables and obtain some new results, which extend some earlier ones for NA random variables.