Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences
We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale diffe...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/572493 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849686110861524992 |
|---|---|
| author | Xuejun Wang Shuhe Hu Wenzhi Yang Xinghui Wang |
| author_facet | Xuejun Wang Shuhe Hu Wenzhi Yang Xinghui Wang |
| author_sort | Xuejun Wang |
| collection | DOAJ |
| description | We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011). |
| format | Article |
| id | doaj-art-b885db8d78e1467f838a43347332dfaa |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b885db8d78e1467f838a43347332dfaa2025-08-20T03:22:49ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/572493572493Convergence Rates in the Strong Law of Large Numbers for Martingale Difference SequencesXuejun Wang0Shuhe Hu1Wenzhi Yang2Xinghui Wang3School 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 study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).http://dx.doi.org/10.1155/2012/572493 |
| spellingShingle | Xuejun Wang Shuhe Hu Wenzhi Yang Xinghui Wang Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences Abstract and Applied Analysis |
| title | Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences |
| title_full | Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences |
| title_fullStr | Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences |
| title_full_unstemmed | Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences |
| title_short | Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences |
| title_sort | convergence rates in the strong law of large numbers for martingale difference sequences |
| url | http://dx.doi.org/10.1155/2012/572493 |
| work_keys_str_mv | AT xuejunwang convergenceratesinthestronglawoflargenumbersformartingaledifferencesequences AT shuhehu convergenceratesinthestronglawoflargenumbersformartingaledifferencesequences AT wenzhiyang convergenceratesinthestronglawoflargenumbersformartingaledifferencesequences AT xinghuiwang convergenceratesinthestronglawoflargenumbersformartingaledifferencesequences |