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math.PR2025
Polynomial Stein operators: a noncommutative algebra perspective
Ehsan Azmoodeh, Dario Gasbarra, Robert E. Gaunt
In this paper, we make a novel connection between Stein's method and noncommutative algebra by viewing polynomial Stein operators (Stein operators with polynomial coefficients) as…
math.PR2024
Probabilistic Cauchy Functional Equations
Ehsan Azmoodeh, Noah Beelders, Yuliya Mishura
In this short note, we introduce probabilistic Cauchy functional equations, specifically, functional equations of the following form: $$ f(X_1 + X_2) \stackrel{d}{=} f(X_1) + f(X_2…