Intertwinings and Stein’s factors for birth-death processes

Abstract: In this talk, I will present intertwinings between Markov processes and gradients, which are functional relations relative to the space-derivative of a Markov semigroup. I will recall the first-order relation , in the continuous case for diffusions and in the discrete case for birth-death processes, and introduce a new second-order relation for a discrete Laplacian. As the main application, new quantitative bounds on the Stein factors of discrete distributions are provided. Stein’s factors are a key component of Stein’s method, a collection of techniques to bound the distance between probability distribution.