Nested distance for stagewise-independent processes

TL;DR

This paper proves that for stagewise-independent processes, the nested distance simplifies to the sum of Wasserstein distances between stage-wise marginals, providing a computationally efficient way to compare such processes.

Contribution

The paper establishes a theoretical equivalence between nested distance and sum of Wasserstein distances for stagewise-independent processes, simplifying their analysis.

Findings

Nested distance equals sum of Wasserstein distances for stagewise-independent processes

Provides a new theoretical insight into process comparison metrics

Simplifies computation of process distances in stochastic modeling

Abstract

We prove that, for two discrete-time stagewise-independent processes with a stagewise metric, the nested distance is equal to the sum of the Wasserstein distances between the marginal distributions of each stage.