Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 2, Pages 135-140

On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables

André Adler

Illinois Institute of Technology, Chicago 60616, IL, USA

Received 1 January 1989; Revised 1 December 1989

Copyright © 1990 André Adler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For weighted sums of independent and identically distributed random variables, conditions are placed under which a generalized law of the iterated logarithm cannot hold, thereby extending the usual nonweighted situation.