Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T21:49:25.974Z Has data issue: false hasContentIssue false
  • English
  • Français

On the converse to the iterated logarithm law

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Extract

Let Xi, i = 1, 2, 3,… be a sequence of independent and identically distributed random variables with law ℓ(X) and write. if EX= 0 and EX2=σ2< ∞, the law of the iterated logarithm (Hartman and Wintner [1]) tells us that

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 210 - 215
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Hartman, P. and Wintner, A. (1941) On the law of the iterated logarithm. Amer. J. Math. 63, 169–176.Google Scholar
[2] Loève, M. (1963) Probability Theory. 3rd edition. Van Nostrand, New York.Google Scholar
[3] Stone, C. (1966) The growth of a recurrent random walk. Ann. Math. Statist. 37, 1040–1041.Google Scholar
[4] Strassen, V. (1966) A converse to the law of the iterated logarithm. Z. Wahrscheinlichkeitsth. 4, 265–268.Google Scholar