Multivariate stable approximation in Wasserstein distance by Stein's method

Abstract

By a delicate analysis for the Stein's equation associated to the $\alpha$-stable law approximation with $\alpha \in (0,2)$, we prove a quantitative stable central limit theorem in Wasserstein type distance, which generalizes the results in the series of work \cite{Xu19, CNX19+,CNXYZ19+} from the univariate case to the multiple variate case. From an explicit computation for Pareto's distribution, we see that the rate of our approximation is sharp. The analysis of the Stein's equation is new and has independent interest.

References in corpus (2)

• On Stein's Method for Multivariate Self-Decomposable Laws
• Non-integrable stable approximation by Stein's method

Cited by in corpus (2)

• A diffusion approach to Stein's method on Riemannian manifolds
• Steady-state diffusion approximations of Markov chains: error analysis via the discrete Poisson equation