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
The influence of extremes on the law of the iterated logarithm
Download PDF
Download PDF
  • Published: February 1988

The influence of extremes on the law of the iterated logarithm

  • Philip S. Griffin1 

Probability Theory and Related Fields volume 77, pages 241–270 (1988)Cite this article

  • 80 Accesses

  • 5 Citations

  • Metrics details

Summary

We investigate the law of the iterated logarithm for the partial sum of independent identically distributed random variables when the r n largest summands are excluded.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

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

    Google Scholar 

  2. Csörgõ, S., Horvàth, L., Mason, D.: What portion of the sample makes a partial sum asymptotically stable or normal? Probab. Th. Rel. Fields, 72, 1–16 (1986)

    Google Scholar 

  3. Feller, W.: An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech. 18, 343–355 (1968)

    Google Scholar 

  4. Griffin, P.S.: Probability estimates for the small deviations of d-dimensional random walk. Ann. Probab. 11, 939–952 (1983)

    Google Scholar 

  5. Griffin, P.S.: Laws of the iterated logarithm for symmetric stable processes. Z. Wahrscheinlichkeitstheor. verw. Geb. 68, 271–285 (1985)

    Google Scholar 

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

    Google Scholar 

  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. Probab. 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. Reference deleted

  11. Mori, T.: Stability for sums of i.i.d. random variables when extreme terms are excluded. Z. Wahrscheinlichkeitstheor. verw. Geb. 40, 159–167 (1977)

    Google Scholar 

  12. Mori, T.: On the limit distribution of lightly trimmed sums. Math. Proc. Camb. Philos. Soc. 96, 507–516 (1984)

    Google Scholar 

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

    Google Scholar 

  14. Pruitt, W.E.: Sums of independent random variables with extreme terms excluded. Reference deleted

  15. Griffin, P.S., Pruitt, W.E.: The central limit problem for trimmed sums. Math. Proc. Camb. Philos. Soc. 102, 329–349 (1987)

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, 13210, Syracuse, NY, USA

    Philip S. Griffin

Authors
  1. Philip 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 MCS-83-03297; A.M.S. 1980 Subject Classification 60F 15

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Griffin, P.S. The influence of extremes on the law of the iterated logarithm. Probab. Th. Rel. Fields 77, 241–270 (1988). https://doi.org/10.1007/BF00334040

Download citation

  • Received: 15 June 1985

  • Revised: 19 October 1987

  • Issue Date: February 1988

  • DOI: https://doi.org/10.1007/BF00334040

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
  • Iterate Logarithm
  • Large Summand
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