文章基本信息

标题：Wasserstein and total variation distance between marginals of Lévy processes
本地全文：下载
作者：Ester Mariucci ; Markus Reiß
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：2
页码：2482-2514
DOI：10.1214/18-EJS1456
语种：English
出版社：Institute of Mathematical Statistics
摘要：We present upper bounds for the Wasserstein distance of order $p$ between the marginals of Lévy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds for the total variation distance between the marginals of Lévy processes. Connections to other metrics like Zolotarev and Toscani-Fourier distances are established. The theory is illustrated by concrete examples and an application to statistical lower bounds.