Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates

Octavio Arizmendi; Arturo Jaramillo

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arXiv · 1402.6283

Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates

Octavio Arizmendi·Arturo Jaramillo

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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. 2014-02-25. Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates. https://arxiv.org/abs/1402.6283

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