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Some inequalities for conditional demimartingales and conditional N-demimartingales

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  • Wang, Xinghui
  • Wang, Xuejun

Abstract

In this paper, we establish some maximal inequalities for conditional demi(sub)martingales and minimal inequalities for nonnegative conditional demimartingales. In addition, we get some moment inequalities for conditional N-demimartingales and nonnegative conditional demimartingales by using the conditional Fubini theorem and the conditional Hölder’s inequality. As an application, a strong law of large numbers for conditionally associated random variables is obtained.

Suggested Citation

  • Wang, Xinghui & Wang, Xuejun, 2013. "Some inequalities for conditional demimartingales and conditional N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 700-709.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:700-709
    DOI: 10.1016/j.spl.2012.11.017
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    References listed on IDEAS

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    1. Prakasa Rao, B.L.S., 2012. "Remarks on maximal inequalities for non-negative demisubmartingales," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1388-1390.
    2. 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.
    3. Wang, Jianfeng, 2004. "Maximal inequalities for associated random variables and demimartingales," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 347-354, February.
    4. Christofides, Tasos C. & Hadjikyriakou, Milto, 2012. "Maximal and moment inequalities for demimartingales and N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 683-691.
    5. Christofides, Tasos C. & Hadjikyriakou, Milto, 2009. "Exponential inequalities for N-demimartingales and negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2060-2065, October.
    6. Hu, Shuhe & Wang, Xuejun & Yang, Wenzhi & Zhao, Ting, 2009. "The Hjek-Rnyi-type inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 884-888, April.
    7. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    8. 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.
    9. Hadjikyriakou, Milto, 2011. "Marcinkiewicz-Zygmund inequality for nonnegative N-demimartingales and related results," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 678-684, June.
    10. 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. Yuan, Demei & Hu, Xuemei, 2015. "A conditional version of the extended Kolmogorov–Feller weak law of large numbers," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 99-107.

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