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Chinese Annals of Mathematics, Series B

, Volume 36, Issue 6, pp 957–968 | Cite as

Chow-type maximal inequality for conditional demimartingales and its applications

  • Xuejun WangEmail author
  • Shijie Wang
  • Chen Xu
  • Shuhe Hu
Article

Abstract

In this paper, the Chow-type maximal inequality for conditional demimartingales is established. By using the Chow-type maximal inequality, the authors provide the maximal inequality for conditional demimartingales based on concave Young functions. At last, the moment inequalities for conditional demimartingales are established.

Keywords

Conditional demimartingales Chow-type maximal inequality Concave Young functions 

2000 MR Subject Classification

60E15 60E05 60G48 

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References

  1. [1]
    Newman, C. M. and Wright, A. L., Associated random variables and martingale inequalities, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 59(3), 1982, 361–371.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Christofides, T. C., Maximal inequalities for demimartingales and a strong law of large numbers, Statistics and Probability Letters, 50(4), 2000, 357–363.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Christofides, T. C., U-statistics on associated random variables, Journal of Statistical Planning and Inference, 119(1), 2004, 1–15.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Wang, J. F., Maximal inequalities for associated random variables and demimartingales, Statistics and Probability Letters, 66(3), 2004, 347–354.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Hu, S. H., Wang, X. J., Yang, W. Z. and Zhao, T., The Hàjek-Rènyi-type inequality for associated random variables, Statistics and Probability Letters, 79, 2009, 884–888.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Wang, X. J. and Hu, S. H., Maximal inequalities for demimartingales and their applications, Science in China Series A: Mathematics, 52(10), 2009, 2207–2217.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Wang, X. J., Hu, S. H., Zhao, T. and Yang, W. Z., Doob’s type inequality and strong law of large numbers for demimartingales, Journal of Inequalities and Applications, 2010, 2010, Article ID 838301, 11 pages.Google Scholar
  8. [8]
    Prakasa Rao, B. L. S., On some maximal inequalities for demisubmartingales and N-demisuper martingales, Journal of Inequalities in Pure and Applied Mathematics, 8(4), 2007, Article ID 112, 17 pages.Google Scholar
  9. [9]
    Prakasa Rao, B. L. S., Remarks on maximal inequalities for non-negative demisubmartingales, Statistics and Probability Letters, 82(7), 2012, 1388–1390.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Prakasa Rao, B. L. S., Associated Sequences, Demimartingales and Nonparametric Inference, Springer- Verlag, Basel AG, 2012.zbMATHCrossRefGoogle Scholar
  11. [11]
    Christofides, T. C., Maximal inequalities for N-demimartingales, Archives of Inequalities and Applications, 50(1), 2003, 397–408.Google Scholar
  12. [12]
    Prakasa Rao, B. L. S., On some inequalities for N-demimartingales, Journal of the Indian Society of Agricultural Statistics, 57, 2004, 208–216.MathSciNetGoogle Scholar
  13. [13]
    Christofides, T. C. and Hadjikyriakou, M., Exponential inequalities for N-demimartingales and negatively associated random varibles, Statistics and Probability Letters, 79(19), 2009, 2060–2065.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    Christofides, T. C. and Hadjikyriakou, M., Maximal and moment inequalities for demimartingales and N-demimartingales, Statistics and Probability Letters, 82(3), 2012, 683–691.zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    Hadjikyriakou, M., Marcinkiewicz-Zygmund inequality for nonnegative N-demimartingales and related results, Statistics and Probability Letters, 81(6), 2011, 678–684.zbMATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    Wang, X. J., Hu, S. H., Prakasa Rao, B. L. S. and Yang, W. Z., Maximal inequalities for N-demimartingale and strong law of large numbers, Statistics and Probability Letters, 81(9), 2011, 1348–1353.zbMATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    Hu, S. H., Wang, X. H., Yang, W. Z. and Wang, X. J., Some inequalities for demimartingales and Ndemimartingales, Statistics and Probability Letters, 82(2), 2012, 232–239.zbMATHMathSciNetCrossRefGoogle Scholar
  18. [18]
    Hadjikyriakou, M., Probability and Moment Inequalities for Demimartingales and Associated Random Variables, Ph. D. Dissertation, Department of Mathematics and Statistics, University of Cyprus, Nicosia, 2010.Google Scholar
  19. [19]
    Yuan, D. M. and Yang, Y. K., Conditional versions of limit theorems for conditionally associated random variables, Journal of Mathematical Analysis and Applications, 376(1), 2011, 282–293.zbMATHMathSciNetCrossRefGoogle Scholar
  20. [20]
    Roussas, G. G., On conditional independence, mixing, and association, Stochastic Analysis and Applications, 26(6), 2008, 1274–1309.zbMATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    Prakasa Rao, B. L. S., Conditional independence, conditional mixing and conditional association, Annals of the Institute of Statistical Mathematics, 61(2), 2009, 441–460.zbMATHMathSciNetCrossRefGoogle Scholar
  22. [22]
    Agbeko, N. K., Concave function inequalities for sub-(super-)martingales, Ann. Univ. Sci. Budapest, Sect. Math., 29, 1986, 9–17.zbMATHMathSciNetGoogle Scholar

Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiChina

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