Inspired by Lemma 3.1 in [4], where a connection between the Gaussian Wick product and the classic convolution product is shown, we prove that the Wick product associated to the Poisson distribution is related to the discrete convolution and hence to the law of the sum of discrete independent random variables. The proof of the main result is based on elementary probabilistic tools and on the properties of the Poisson-Charlier polynomials.

On a connection between the Poissonian Wick product and the discrete convolution

LANCONELLI, ALBERTO;SPORTELLI, LUIGI
2011

Abstract

Inspired by Lemma 3.1 in [4], where a connection between the Gaussian Wick product and the classic convolution product is shown, we prove that the Wick product associated to the Poisson distribution is related to the discrete convolution and hence to the law of the sum of discrete independent random variables. The proof of the main result is based on elementary probabilistic tools and on the properties of the Poisson-Charlier polynomials.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/20810
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