Convergence of the Fourth Moment and Infinite Divisibility
Probability
2013-06-13 v1
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.
Keywords
Cite
@article{arxiv.1306.2674,
title = {Convergence of the Fourth Moment and Infinite Divisibility},
author = {Octavio Arizmendi},
journal= {arXiv preprint arXiv:1306.2674},
year = {2013}
}
Comments
10 pages