Convergence of the Fourth Moment and Infinite Divisibility

Octavio Arizmendi

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arXiv · 1306.2674

Convergence of the Fourth Moment and Infinite Divisibility

Octavio Arizmendi

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Abstract

In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our results include infinitely divisible measures with respect to classical, free, Boolean and monotone convolution. A similar criterion is proved for compound Poissons with jump distribution supported on a finite number of atoms. In particular, this generalizes recent results of Nourdin and Poly.

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Octavio Arizmendi. 2013-06-11. Convergence of the Fourth Moment and Infinite Divisibility. https://arxiv.org/abs/1306.2674

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