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

Author

Listed:
  • Zhiyong Chen
  • Shuhe Hu
  • Jimin Ling
  • Xuejun Wang

Abstract

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.

Suggested Citation

  • Zhiyong Chen & Shuhe Hu & Jimin Ling & Xuejun Wang, 2013. "Strong Convergence Properties and Strong Stability for Weighted Sums of AANA Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:295041
    DOI: 10.1155/2013/295041
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    References listed on IDEAS

    as
    1. Aiting Shen & Ranchao Wu, 2013. "Strong and Weak Convergence for Asymptotically Almost Negatively Associated Random Variables," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, February.
    2. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Jiangfeng Wang & Qunying Wu, 2011. "Strong Laws of Large Numbers for Arrays of Rowwise NA and LNQD Random Variables," Journal of Probability and Statistics, Hindawi, vol. 2011, pages 1-10, December.
    4. André Adler, 1990. "On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables," International Journal of Stochastic Analysis, Hindawi, vol. 3, pages 1-6, January.
    5. Wang, Xuejun & Hu, Shuhe & Prakasa Rao, B.L.S. & Yang, Wenzhi, 2011. "Maximal inequalities for N-demimartingale and strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1348-1353, September.
    6. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
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