## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 893906, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412273266

Digital Object Identifier
doi:10.1155/2014/893906

Mathematical Reviews number (MathSciNet)
MR3191074

Zentralblatt MATH identifier
07023255

#### Citation

Yang, Wenzhi; Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe. The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application. Abstr. Appl. Anal. 2014 (2014), Article ID 893906, 7 pages. doi:10.1155/2014/893906. https://projecteuclid.org/euclid.aaa/1412273266

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