Limit Theorems in Mallows Distance for Processes with Gibssian Dependence

TL;DR

This paper investigates how convergence in distribution relates to Mallows distance for processes with Gibbsian dependence, extending invariance principles for positively associated variables and including applications.

Contribution

It extends invariance principles for sequences with FKG property to processes with Gibbsian dependence structures, connecting distributional convergence and Mallows distance.

Findings

Extended invariance principles to Gibbsian dependent processes

Established links between convergence in distribution and Mallows distance

Applied results to processes with Gibbsian dependence

Abstract

In this paper, we explore the connection between convergence in distribution and Mallows distance in the context of positively associated random variables. Our results extend some known invariance principles for sequences with FKG property. Applications for processes with Gibbssian dependence structures are included.