Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Non-classical law of the iterated logarithm behaviour for trimmed sums
Download PDF
Download PDF
  • Published: June 1988

Non-classical law of the iterated logarithm behaviour for trimmed sums

  • Phillip S. Griffin1 

Probability Theory and Related Fields volume 78, pages 293–319 (1988)Cite this article

  • 61 Accesses

  • 3 Citations

  • Metrics details

Summary

We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r n largest summands are excluded, where r n=o(log logn). This complements earlier work in which the case log logn=O(rn) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Breiman, L.: Probability. Reading, Mass.: Addison-Wesley 1968

    Google Scholar 

  2. Feller, W.: On regular variation and local limit theorems. Proceedings Fifth Berkeley Symposium Math. Statist. Probab. Vol. II, Part 1, pp. 373–3881967

    Google Scholar 

  3. Griffin, P.S.: The influence of extremes on the law of the iterated logarith. Prob. Th. Rel. Fields 77, 241–270 (1988)

    Google Scholar 

  4. Griffin, P.S., Jain, N.C., Pruitt, W.E.: Approximate local limit theorems for laws outside domains of attractions. Ann. Probab. 12, 45–63 (1984)

    Google Scholar 

  5. Haeusler, E., Mason, D.M.: Law of the iterated logarithm for sums of the middle portion of the sample. Math. Proc. Camb. Philos. Soc. 101, 301–312 (1987)

    Google Scholar 

  6. Hahn, M.G., Kuelbs, J.: Asymptotic normality and the L.I.L. for trimmed sums: the general case. Preprint (1986)

  7. Kesten, H.: Sums of independent random variables-without moment conditions. Ann. Math. Stat. 43, 701–732 (1972)

    Google Scholar 

  8. Kuelbs, J., Ledoux, M.: Extreme values and the law of the iterated logarithm. Prob. Th. Rel. Fields, 74, 319–340 (1987)

    Google Scholar 

  9. Loeve, M.: Probability Theory I, 4th edn., Berlin Heidelberg New York: Springer Verlag 1977

    Google Scholar 

  10. Maller, R.A.: Some almost sure properties of trimmed sums. Preprint (1984)

  11. Maller, R.A., Resnick, S.I.: Limiting behaviour of sums and the term of maximum modulus. Proc. London Math. Soc. III Ser. 49, 385–422 (1984)

    Google Scholar 

  12. Pruitt, W.E.: General one-sided laws of the iterated logarithm. Ann. Probab. 9, 1–48 (1981)

    Google Scholar 

  13. Pruitt, W.E.: Sums of independent random variables with extreme terms excluded. Preprint (1986)

  14. Spitzer, F.: Principles of Random Walk. Wokingham New York Toronto Melbourne: Van Nostrand 1964

    Google Scholar 

  15. Klass, M.J.: An interpretation of the finite mean L.I.L. norming constants. Theory Probab. Appl. 29, 599–601 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, 13244-1150, Syracuse, NY, USA

    Phillip S. Griffin

Authors
  1. Phillip S. Griffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by NSF Grant DMS-8501732

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Griffin, P.S. Non-classical law of the iterated logarithm behaviour for trimmed sums. Probab. Th. Rel. Fields 78, 293–319 (1988). https://doi.org/10.1007/BF00322025

Download citation

  • Received: 01 April 1986

  • Revised: 08 January 1988

  • Issue Date: June 1988

  • DOI: https://doi.org/10.1007/BF00322025

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Wide Class
  • Iterate Logarithm
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature