1,745 research outputs found
Convergence of the Fourth Moment and Infinite Divisibility
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.Comment: 10 page
Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates
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.Comment: 12 page
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