Georgia Institute of Technology College of Sciences

Stein's method is a powerful technique to quantify proximity between probability measures, which has been mainly developed in the Gaussian and the Poisson settings. It is based on a covariance representation which completely characterizes the target probability measure. In this talk, I will present some recent unifying results regarding Stein's method for infinitely divisible laws with finite first moment. In particular, I will present new quantitative results regarding Compound Poisson approximation of infinitely divisible laws, approximation of self-decomposable distributions by sums of independent summands and stability results for self-decomposable laws which satisfy a second moment assumption together with an appropriate Poincaré inequality. This is based on joint works with Christian Houdré.