A connection between the Poissonian Wick product and the discrete convolution

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.

Locations

• Communications on Stochastic Analysis - View - PDF