Abstract and Applied Analysis

Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences

Xuejun Wang, Shuhe Hu, Wenzhi Yang, and Xinghui Wang

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Abstract

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).

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 572493, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495801

Digital Object Identifier
doi:10.1155/2012/572493

Mathematical Reviews number (MathSciNet)
MR2955034

Zentralblatt MATH identifier
1253.60045

Citation

Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui. Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences. Abstr. Appl. Anal. 2012 (2012), Article ID 572493, 13 pages. doi:10.1155/2012/572493. https://projecteuclid.org/euclid.aaa/1355495801


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