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

Author

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  • 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, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:893906
    DOI: 10.1155/2014/893906
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