Multivariate stable approximation in Wasserstein distance by Stein's method
Probability
2023-01-26 v2
Abstract
By a delicate analysis for the Stein's equation associated to the -stable law approximation with , 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.
Keywords
Cite
@article{arxiv.1911.12917,
title = {Multivariate stable approximation in Wasserstein distance by Stein's method},
author = {Peng Chen and Ivan Nourdin and Lihu Xu and Xiaochuan Yang},
journal= {arXiv preprint arXiv:1911.12917},
year = {2023}
}