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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/893906 |
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| _version_ | 1832563188496859136 |
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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. |
| format | Article |
| id | doaj-art-e90a1bebd65f4f14ae752904826287fb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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