Rubinstein distance on configurations spaces

TL;DR

This paper introduces a Stein's method-inspired approach to bound the Rubinstein distance between probability measures on configuration spaces, demonstrating optimal Poisson process approximation by matching intensities.

Contribution

It provides a novel upper-bound technique for Rubinstein distance on configuration spaces and applies it to optimize Poisson process approximation.

Findings

Upper-bound of Rubinstein distance derived

Optimal Poisson approximation achieved by equating intensities

Method applicable to absolutely continuous measures on configuration spaces

Abstract

By a method inspired of the Stein's method, we derive an upper-bound of the Rubinstein distance between two absolutely continuous probability measures on configurations space. As an application, we show that the best way to approximate a Modulated Poisson Process (see below for the definition) by a Poisson process is to equate their intensity.