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

Xuejun Wang | Zendy; Shuhe Hu | Zendy; Wenzhi Yang | Zendy; Xinghui Wang | Zendy

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

Author(s) -

Xuejun Wang,

Shuhe Hu,

Wenzhi Yang,

Xinghui Wang

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/572493

Subject(s) - mathematics , martingale difference sequence , martingale (probability theory) , local martingale , law of large numbers , sequence (biology) , rate of convergence , pure mathematics , mathematical analysis , random variable , statistics , key (lock) , ecology , biology , genetics

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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