Skip to main content
SpringerLink
Log in

Invariance principles for martingales and sums of independent random variables

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

References

  1. Basu, A.K.: A note on Strassen's version of the law of the iterated logarithm. Proc. AMS41, 596–601 (1973)

    Google Scholar 

  2. Feller, W.: The general form of the so-called law of the iterated logarithm. Trans. Am. Math. Soc.54, 373–402 (1943)

    Google Scholar 

  3. Hall, P., Heyde, C.C.: Martingale limit theory and its applications. New York: Academic Press 1980

    Google Scholar 

  4. Jain, N.C., Jogdeo, K., Stout, W.F.: Upper and lower functions for martingales and mixing processes. Ann. Probab.3, 119–145 (1975)

    Google Scholar 

  5. Major, P.: Approximation of partial sum of i.i.d.r.v.s. when the summands have only two moments. Z. Wahrscheinlichkeitstheor. Verw. Geb.32, 221–229 (1976)

    Google Scholar 

  6. Major, P.: A note on Kolmogorov's law of the iterated logarithm. Stud. Sci. Math. Hung.12, 161–167 (1977)

    Google Scholar 

  7. Stout, W.F.: A martingale analogue of Kolmogorov's law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.15, 279–290 (1970)

    Google Scholar 

  8. Stout, W.F.: The Hartman-Wintner law of the iterated law of the iterated logarithm for martingales. Ann. Math. Statist.41, 2158–2160 (1970)

    Google Scholar 

  9. Stout, W.F.: Almost sure convergence. New York: Academic Press 1974

    Google Scholar 

  10. Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 211–226 (1964)

    Google Scholar 

  11. Strassen, V.: Almost sure behavior of sums of independent random variables and martingales. Proc. 5th Berkeley Symposium. Math. Stat. Probab. Vol.II, Part 1, 314–343 (1965)

    Google Scholar 

  12. Teicher, H.: On the law of the iterated logarithm. Ann. Probab.2, 714–728 (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 61801, Urbana, IL, USA

    Walter Philipp & William Stout

Authors
  1. Walter Philipp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Stout
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by National Science Foundation (USA) Grants DMS 82-03602, MCS 82-01771, and DMS 85-03321

Rights and permissions

Reprints and permissions

About this article

Cite this article

Philipp, W., Stout, W. Invariance principles for martingales and sums of independent random variables. Math Z 192, 253–264 (1986). https://doi.org/10.1007/BF01179427

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01179427

Keywords

Search

Navigation