Convergence of the fourth moment and infinite divisibility

• Autorzy: Arizmendi O.
• Języki publikacji: EN

Abstrakty

EN

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 (2012).

Słowa kluczowe

EN

Bercovici-Pata bijections; Boolean convolution; free convolution; monotone convolution; infinite divisibility

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 201--212
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Arizmendi O.

• Department of Mathematics, Saarland University, Saarbrücken, Germany

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).