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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 44, Pages 2771-2786

Moment inequalities connected with accompanying Poisson laws in Abelian groups

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia

Received 25 November 2002

Copyright © 2003 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.


We obtain exact inequalities which connect moments of some functions of sums of independent random variables taking values in a measurable Abelian group and those for the accompanying infinitely divisible laws. Some applications to empirical processes are studied.