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2014 The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
Wenzhi Yang, Xinghui Wang, Xiaoqin Li, Shuhe Hu
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/893906

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.

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Wenzhi Yang. Xinghui Wang. Xiaoqin Li. Shuhe Hu. "The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/893906

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023255
MathSciNet: MR3191074
Digital Object Identifier: 10.1155/2014/893906

Rights: Copyright © 2014 Hindawi

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