Open Access
August, 1974 On the Law of the Iterated Logarithm
Henry Teicher
Ann. Probab. 2(4): 714-728 (August, 1974). DOI: 10.1214/aop/1176996614


A triumvirate of sufficient conditions is given for unbounded, independent random variables to obey the Law of the Iterated Logarithm (LIL). As special cases, new results for weighted i.i.d. random variables and the Hartman-Wintner theorem are obtained. Necessity of finite variance for the two-sided LIL is shown to carry over for a large class of weighted i.i.d. random variables and the Marcinkiewicz-Zygmund example is generalized, simplified and clarified.


Download Citation

Henry Teicher. "On the Law of the Iterated Logarithm." Ann. Probab. 2 (4) 714 - 728, August, 1974.


Published: August, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.60013
MathSciNet: MR370715
Digital Object Identifier: 10.1214/aop/1176996614

Primary: 60F15

Keywords: Hartman condition , Marcinkiewicz-Zygmund growth , Two-Sided iterated logarithm law , weighted i.i.d. random variables

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 4 • August, 1974
Back to Top