On a new Sheffer class of polynomials related to normal product distribution

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Azmoodeh , E & Gasbarra , D 2019 , ' On a new Sheffer class of polynomials related to normal product distribution ' , Theory of Probability and Mathematical Statistics , vol. 98 , no. 1 , pp. 51-71 . https://doi.org/10.1090/tpms/1062

Title: On a new Sheffer class of polynomials related to normal product distribution
Author: Azmoodeh, Ehsan; Gasbarra, Dario
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019
Language: eng
Number of pages: 21
Belongs to series: Theory of Probability and Mathematical Statistics
ISSN: 0094-9000
URI: http://hdl.handle.net/10138/307997
Abstract: In this paper, using the Stein operator R-infinity given in [17], associated with the normal product distribution living in the second Wiener chaos, we introduce a new class of polynomials P-infinity:= {P-n(x) = R(infinity)(n)1 : n >= 1}. We analyze in details the polynomials class P-infinity, and relate it to Rota's Umbral calculus by showing that it is a Sheffer family and enjoys many interesting properties. Lastly, we study the connection between the polynomial class P-infinity and the non-central probabilistic limit theorems within the second Wiener chaos.
Subject: Second Wiener chaos
normal product distribution
cumulants/moments
weak convergence
Malliavin calculus
Sheffer polynomials
umbral calculus
RANDOM-VARIABLES
112 Statistics and probability
111 Mathematics
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