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

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 weight...

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Main Authors: Wenzhi Yang, Xinghui Wang, Xiaoqin Li, Shuhe Hu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/893906
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author Wenzhi Yang
Xinghui Wang
Xiaoqin Li
Shuhe Hu
author_facet Wenzhi Yang
Xinghui Wang
Xiaoqin Li
Shuhe Hu
author_sort Wenzhi Yang
collection DOAJ
description 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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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-e90a1bebd65f4f14ae752904826287fb2025-02-03T01:20:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/893906893906The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its ApplicationWenzhi Yang0Xinghui Wang1Xiaoqin Li2Shuhe Hu3School of Mathematical Science, Anhui University, Hefei 230039, ChinaSchool of Mathematical Science, Anhui University, Hefei 230039, ChinaSchool of Mathematical Science, Anhui University, Hefei 230039, ChinaSchool of Mathematical Science, Anhui University, Hefei 230039, ChinaWe 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.http://dx.doi.org/10.1155/2014/893906
spellingShingle Wenzhi Yang
Xinghui Wang
Xiaoqin Li
Shuhe Hu
The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
Abstract and Applied Analysis
title The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
title_full The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
title_fullStr The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
title_full_unstemmed The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
title_short The Convergence of Double-Indexed Weighted Sums of Martingale Differences and Its Application
title_sort convergence of double indexed weighted sums of martingale differences and its application
url http://dx.doi.org/10.1155/2014/893906
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