Almost sure invariance principle for the Kantorovich distance between the empirical and the marginal distributions of strong mixing sequences

Jérôme Dedecker; Florence Merlevède

doi:10.1016/j.spl.2020.108991

paper

Almost sure invariance principle for the Kantorovich distance between the empirical and the marginal distributions of strong mixing sequences

arXiv:2301.05512 · doi:10.1016/j.spl.2020.108991

Abstract

We prove a strong invariance principle for the Kantorovich distance between the empiricaldistribution and the marginal distribution of stationary $α$ -mixing sequences.