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.
Lanconelli, A., Sportelli, L. (2011). On a connection between the Poissonian Wick product and the discrete convolution. COMMUNICATIONS ON STOCHASTIC ANALYSIS, 5(4), 689-699 [10.31390/cosa.5.4.06].
On a connection between the Poissonian Wick product and the discrete convolution
Lanconelli A
Investigation
;
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.| File | Dimensione | Formato | |
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