Multivariate stable approximation in Wasserstein distance by Stein's method

Understand

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.