Skip to main content
SpringerLink
Log in

A general law of precise asymptotics for the complete moment convergence

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of i.i.d. random variables, which includes complete convergence as a special case. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results of Liu and Lin in 2006.

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. Cheng, F. Y. and Wang, Y. B., Precise asymptotics of partial sums for IID and NA sequences (in Chinese), Acta. Math. Sin., Ser. A, 45(5), 2004, 965–972.

    MathSciNet  Google Scholar 

  2. Gut, A. and Spătaru, A., Precise asymptotics in the Baum-Katz and Davis law of large numbers, J. Math. Anal. Appl., 248, 2000, 233–246.

    Article  MATH  MathSciNet  Google Scholar 

  3. Gut, A. and Spătaru, A., Precise asymptotics in the law of the iterated logarithm, Ann. Prob., 28, 2000, 1870–1883.

    Article  MATH  Google Scholar 

  4. Hall, P. and Heyde, C. C., Martingale Limit Theory and Its Application, Academic Press, New York, 1980.

    MATH  Google Scholar 

  5. Heyde, C. C., A supplement to the strong law of large numbers, J. Appl. Prob., 12, 1975, 173–175.

    Article  MATH  MathSciNet  Google Scholar 

  6. Hsu, P. L. and Robbins, H., Complete convergence and the strong law of large numbers, Proc. Nat. Acad. Sci. USA, 33, 1947, 25–31.

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, W. D. and Lin, Z. Y., Precise asymptotics for a new kind of complete moment convergence, Stat. Prob. Lett, 76, 2006, 1787–1799.

    Article  MATH  MathSciNet  Google Scholar 

  8. Nagaev, S. V., Large deviations of sums of independent random variables, Ann. Prob., 7(5), 1979, 745–789.

    Article  MATH  MathSciNet  Google Scholar 

  9. Pang, T. X. and Wang, J. F., Precise asymptotics in Chung’s law of the iterated logarithm via self-normalization (in Chinese), Chin. Ann. Math., 28A(4), 2007, 507–518.

    MathSciNet  Google Scholar 

  10. Pruss, A. R., A two-sided estimate in the Hsu-Robbins-Erdos law of large numbers, Stoch. Proc. Appl., 70, 1997, 173–180.

    Article  MATH  MathSciNet  Google Scholar 

  11. Spătaru, A., Precise asymptotics in Spitzer’s law of large numbers, J. Theor. Prob., 12, 1999, 811–819.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Jilin University (Qianwei Campus), Changchun, 130012, China

    Yong Zhang, Xiaoyun Yang & Zhishan Dong

Authors
  1. Yong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoyun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhishan Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhishan Dong.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10571073) and the 985 Program of Jilin University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Y., Yang, X. & Dong, Z. A general law of precise asymptotics for the complete moment convergence. Chin. Ann. Math. Ser. B 30, 77–90 (2009). https://doi.org/10.1007/s11401-007-0309-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-007-0309-6

Keywords

2000 MR Subject Classification

Search

Navigation