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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 397-404

On the characteristic function of a sum of M-dependent random variables

Faculty of Management Sciences, The Ohio State University, Columbus 43210, Ohio, USA

Received 8 October 1985

Copyright © 1986 Hindawi Publishing Corporation. 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.


Let S=f1+f2++fn be a sum of 1-dependent random variables of zero mean. Let σ2=ES2, L=σ31inE|fi|3. There is a universal constant a such that for a|t|L<1, we have|Eexp(itSσ1)|(1+a|t|)sup{(a|t|L)1/4lnL,exp(t2/80)}.This bound is a very useful tool in proving Berry-Esseen theorems.