An algebra of Stein operators

Abstract

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are $k$th degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of $k$ independent symmetric variance-gamma distributed random variables.

20 pages

References in corpus (6)

• Exponential Approximation by Stein's Method and Spectral Graph Theory
• On Stein's Method for Infinitely Divisible Laws With Finite First Moment
• A bound on the 2-Wasserstein distance between linear combinations of independent random variables
• A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence
• Stein characterizations for linear combinations of gamma random variables
• Approximation of stable law in Wasserstein-1 distance by Stein's method

Cited by in corpus (3)

• A bound on the 2-Wasserstein distance between linear combinations of independent random variables
• On products of Gaussian random variables
• Stein characterizations for linear combinations of gamma random variables