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

TL;DR

This paper establishes a strong invariance principle for the Kantorovich distance, measuring the difference between empirical and marginal distributions, specifically for stationary alpha-mixing sequences, advancing understanding of their probabilistic behavior.

Contribution

It introduces a strong invariance principle for the Kantorovich distance in the context of stationary alpha-mixing sequences, a novel result in this area.

Findings

Proves a strong invariance principle for the Kantorovich distance

Applies to stationary alpha-mixing sequences

Enhances understanding of empirical distribution convergence

Abstract

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