On algebraic Stein operators for Gaussian polynomials

The first essential ingredient to build up Stein’s method for a continuous target distribution is identify so-called Stein operator, namely linear differential operator with polynomial coefficients. In this paper, we introduce the notion of algebraic operators (see Definition 3.4), and provide novel find all given order degree random variable form Y=h(X), where X=(X1,…,Xd) has i.i.d. standard Gaussian components h?K[X] coefficients in ring K. Our approach links existence an null controllability certain discrete system. A MATLAB code checks finite time T (the operator), provides control sequences (polynomial operator) maximum m. This paper that connects computational algebra highly complex probability distributions, such as H20(X1), Hp p-th Hermite polynomial. Some examples Hp(X1), p=3,4,5,6, are gathered Appendix many other Supplementary Information.