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, 1-7

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:893906

DOI: 10.1155/2014/893906

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