International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 781385 | https://doi.org/10.1155/S0161171286000492

Wansoo T. Rhee, "On the characteristic function of a sum of M-dependent random variables", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 781385, 8 pages, 1986. https://doi.org/10.1155/S0161171286000492

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

Received08 Oct 1985

Abstract

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.

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.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views561
Downloads577
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.