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The Convergence of Double‐Indexed Weighted Sums of Martingale Differences and Its Application

Author

Listed:
  • Wenzhi Yang
  • Xinghui Wang
  • Xiaoqin Li
  • Shuhe Hu

Abstract

We investigate the complete moment convergence of double‐indexed weighted sums of martingale differences. Then it is easy to obtain the Marcinkiewicz‐Zygmund‐type strong law of large numbers of double‐indexed weighted sums of martingale differences. Moreover, the convergence of double‐indexed weighted sums of martingale differences is presented in mean square. On the other hand, we give the application to study the convergence of the state observers of linear‐time‐invariant systems and present the convergence with probability one and in mean square.

Suggested Citation

  • Wenzhi Yang & Xinghui Wang & Xiaoqin Li & Shuhe Hu, 2014. "The Convergence of Double‐Indexed Weighted Sums of Martingale Differences and Its Application," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:893906
    DOI: 10.1155/2014/893906
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    References listed on IDEAS

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    1. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, July.
    2. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Subhashis Ghosal & Tapas K. Chandra, 1998. "Complete Convergence of Martingale Arrays," Journal of Theoretical Probability, Springer, vol. 11(3), pages 621-631, July.
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