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...

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Main Authors: Xuejun Wang, Shuhe Hu, Wenzhi Yang, Xinghui Wang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/572493
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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).
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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