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2014 Convergence of the fourth moment and infinite divisibility: quantitative estimates.
Octavio Arizmendi, Arturo Jaramillo
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-3354

Abstract

We give an estimate for the Kolmogorov distance between an infinitely divisible distribution (with mean zero and variance one) and the standard Gaussian distribution in terms of the difference between the fourth moment and 3. In a similar fashion we give an estimate for the Kolmogorov distance between a freely infinitely divisible distribution and the Semicircle distribution in terms of the difference between the fourth moment and 2.

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Octavio Arizmendi. Arturo Jaramillo. "Convergence of the fourth moment and infinite divisibility: quantitative estimates.." Electron. Commun. Probab. 19 1 - 12, 2014. https://doi.org/10.1214/ECP.v19-3354

Information

Accepted: 4 May 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1317.46046
MathSciNet: MR3208324
Digital Object Identifier: 10.1214/ECP.v19-3354

Subjects:
Primary: 46L54
Secondary: 46L50 , 60E07

Keywords: Fourth moment theorem , Free probability , Gaussian distribution , Infinite Divisbility

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