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Maximal inequalities for associated random variables and demimartingales

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  • Wang, Jianfeng

Abstract

In this paper, we establish a maximal inequality for demimartingales which generalizes and improves the main result of Christofides (Statist. Probab. Lett. 50 (2000) 357). The maximal inequality obtained for demimartingales is used as a key inequality to obtain Doob's type inequalities for associated random variables, and for more general demimartingales. At last, we derive a Hájek-Rényi inequality for associated fields.

Suggested Citation

  • Wang, Jianfeng, 2004. "Maximal inequalities for associated random variables and demimartingales," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 347-354, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:347-354
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    References listed on IDEAS

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    1. Christofides, Tasos C., 2000. "Maximal inequalities for demimartingales and a strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 357-363, December.
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    Cited by:

    1. Wang, Xinghui & Wang, Xuejun, 2013. "Some inequalities for conditional demimartingales and conditional N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 700-709.
    2. Wang, Xuejun & Hu, Shuhe & Shen, Yan & Ling, Nengxiang, 2008. "Strong law of large numbers and growth rate for a class of random variable sequences," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3330-3337, December.
    3. Wang, Xuejun & Hu, Shuhe & Prakasa Rao, B.L.S. & Yang, Wenzhi, 2011. "Maximal inequalities for N-demimartingale and strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1348-1353, September.
    4. Hu, Shuhe & Wang, Xinghui & Yang, Wenzhi & Wang, Xuejun, 2012. "Some inequalities for demimartingales and N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 232-239.

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