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

Wenzhi Yang, Xinghui Wang, Xiaoqin Li and Shuhe Hu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/893906

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:893906

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