Skip to main content
SpringerLink
Log in

Almost sure convergence theorem and strong stability for weighted sums of NSD random variables

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, Kolmogorov-type inequality for negatively superadditive dependent (NSD) random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated (NA) sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Joag-Dev, K., Proschan, F.: Negative association of random variables with applications. Ann. Statist., 11, 286–295 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  2. Matula, P.: A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Probab. Lett., 15, 209–213 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gan, S. X.: Strong stability of weighted sums of NA random variables. Int. J. Math. Math. Sci., 6, 975–985 (2005)

    Google Scholar 

  4. Gan, S. X.: Some limit theorems for sequences of pairwise NQD random variables. Acta Math. Sci., 28B(2), 269–281 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Wang, X. J., Li, X. Q., Hu, S. H., et al.: Strong limit theorems for weighted sums of negatively associated random variables. Stoch. Anal. Appl., 29, 1–14 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hu, T. Z.: Negatively superadditive dependence of random variables with applications. Chinese J. Appl. Probab. Statist., 16, 133–144 (2000)

    MathSciNet  MATH  Google Scholar 

  7. Christofides, T. C., Vaggelatou, E.: A connection between supermodular ordering and positive/negative association. J. Multivariate Anal., 88, 138–151 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eghbal, N., Amini, M., Bozorgnia, A.: Some maximal inequalities for quadratic forms of negative superadditive dependence random variables. Statist. Probab. Lett., 80, 587–591 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Eghbal, N., Amini, M., Bozorgnia, A.: On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables. Statist. Probab. Lett., 81, 1112–1120 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kemperman, J. H. B.: On the FKG-inequalities for measures on a partially ordered space. Indag. Math., 39, 313–331 (1977)

    MathSciNet  Google Scholar 

  11. Shao, Q. M.: A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theoret. Probab., 13(2), 343–355 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Science, Anhui University, Hefei, 230039, P. R. China

    Yan Shen, Xue Jun Wang, Wen Zhi Yang & Shu He Hu

Authors
  1. Yan Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue Jun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen Zhi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shu He Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shu He Hu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11171001, 11201001 and 11126176), Natural Science Foundation of Anhui Province (1208085QA03) and Academic Innovation Team of Anhui University (Grant No. KJTD001B)

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shen, Y., Wang, X.J., Yang, W.Z. et al. Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Acta. Math. Sin.-English Ser. 29, 743–756 (2013). https://doi.org/10.1007/s10114-012-1723-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-012-1723-6

Keywords

MR(2010) Subject Classification

Search

Navigation