Skip to main content
Log in

A nonclassical law of iterated logarithm for negatively associated random variables

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal inequality and the subsequence method. This result extends the work of Klesov, Rosalsky (2001) and Shao, Su (1999).

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alam, K., Saxena, K.M.L., Positive dependence in multivariate distributions, Comm. Statist., 1981, A10:1183–1196.

    Google Scholar 

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

    Google Scholar 

  3. Shao Qiman, Su Chun, The law of the iterated logarithm for negatively associated random variables, Stochastic Process Appl., 1999, 83:139–148.

    Article  MATH  Google Scholar 

  4. Klesov, O., Rosalsky, A., A nonclassical law of the iterated logarithm for I.I.D. square integrable random variables, Stochastic Analysis Appl., 1999,83:139–148.

    Google Scholar 

  5. Shao Qiman, A comparison theorem on maximum inequalities between negatively associated and independent random variables, J. Theoret. Probab., 2000, 13:343–356.

    Article  MATH  Google Scholar 

  6. Zhang Lixin, Strassen’s law of the iterated logarithm for negatively associated random vectors, Stochastic Process Appl., 2001, 95:311–328.

    Article  MATH  Google Scholar 

  7. de Acosta, A., A new proof of the Hartman-Wintner law of the iterated logarithm, Ann. Probab., 1983, 11:270–276.

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, Y. A nonclassical law of iterated logarithm for negatively associated random variables. Appl. Math. Chin. Univ. 18, 200–208 (2003). https://doi.org/10.1007/s11766-003-0025-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-003-0025-2

MR Subject Classification

Keywords

Navigation