Journal of Theoretical Probability

, Volume 20, Issue 4, pp 901–915

A Generalization of Strassen’s Functional LIL


DOI: 10.1007/s10959-007-0091-0

Cite this article as:
Einmahl, U. J Theor Probab (2007) 20: 901. doi:10.1007/s10959-007-0091-0


Let X1,X2,… be a sequence of i.i.d. mean zero random variables and let Sn denote the sum of the first n random variables. We show that whenever we have with probability one, lim sup n→∞|Sn|/cn=α0<∞ for a regular normalizing sequence {cn}, the corresponding normalized partial sum process sequence is relatively compact in C[0,1] with canonical cluster set. Combining this result with some LIL type results in the infinite variance case, we obtain Strassen type results in this setting.


Hartman–Wintner LIL Strassen-type results Infinite variance Very slowly varying functions Sums of i.i.d. random variables Strong invariance principle 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Departement WiskundeVrije Universiteit BrusselBrusselBelgium

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