A converse to the law of the iterated logarithm

  • V. Strassen
Article

Keywords

Stochastic Process Probability Theory Mathematical Biology Iterate Logarithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Loève, M.: Probability Theory, The University series in Higher Mathematics, Princeton, 3rd edition (1963).Google Scholar
  2. [2]
    Gnedenko, B. V., and A. N. Kolmogorov: Limit Distributions for Sums of Independent Random Variables, Cambridge, Mass. (1954).Google Scholar
  3. [3]
    Hartman, P., and A. Winter: On the law of the iterated logarithm, Amer. J. Math., 63, 169–176 (1941).Google Scholar
  4. [4]
    Khintchine, A.: über einen Satz der Wahrscheinlichkeitsrechnung, Fundamenta Math., 6, 9–20 (1924).Google Scholar
  5. [5]
    Kolmogorov, A. N.: Das Gesetz des iterierten Logarithmus, Math. Ann. 101, 126–135 (1929).Google Scholar
  6. [6]
    Feller, W.: The law of the iterated logarithm for identically distributed random variables, Ann. of Math., II. Sev. 47, 631–638 (1946).Google Scholar
  7. [7]
    Strassen, V.: An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie verw. Gebiete 3, 211–226 (1964).Google Scholar
  8. [8]
    Hewitt, E., and L. J. Savage: Symmetric measures on Cartesian products, Trans. Amer. math. Soc. 80, 470–501 (1955).Google Scholar
  9. [9]
    Skorokhod, A. B.: Studies in the Theory of Random Processes, Reading, Massachusetts (1965).Google Scholar
  10. [10]
    Feller, W.: A limit theorem for random variables with infinite moments, Amer. J. Math. 68, 257–262 (1946).Google Scholar
  11. [11]
    Chow, Y. S., and H. Robbins: On sums of independent random variables with infinite moments and “fair” games, Proc. nat. Acad. Sci. U.S.A. 47, 330–335 (1961).Google Scholar

Copyright information

© Springer-Verlag 1966

Authors and Affiliations

  • V. Strassen
    • 1
    • 2
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeley 4USA
  2. 2.Institut für Mathematische Statistik der Universität GöttingenGermany

Personalised recommendations