On a characterization of infinitely divisible distributions with Gaussian component

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows that for a large class of distributions with finite variance...

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Bibliographic Details
Published in:arXiv.org 2015-08
Main Authors: Klebanov, Lev B, Volchenkova, Irina V, Kakosyan, Ashot V
Format: Article
Language:English
Subjects:
Approximation
Gaussian distribution
Mathematical analysis
Random variables
Sums
Online Access:Get full text
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Summary:We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows that for a large class of distributions with finite variance stable approximation appears to be better than Gaussian. keywords: infinitely divisible distributions; Gaussian component; approximations of sums of random variables.
ISSN:2331-8422