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2012•Abstract and Applied AnalysisOpen access

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

Xuejun Wang, Xuejun Wang, Shuhe Hu, Xinghui Wang, Xinghui Wang, 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).

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What this paper is about

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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Available 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).

Key concepts: Mathematics, Martingale difference sequence, Martingale (probability theory), Local martingale, Law of large numbers, Sequence (biology), Rate of convergence, Applied mathematics

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