Generalized Wasserstein distance and weak convergence of sublinear expectations

TL;DR

This paper introduces a generalized Wasserstein distance for sets of probability measures and shows it can characterize the weak convergence of sublinear expectations, extending classical concepts to a broader framework.

Contribution

The paper defines a new generalized Wasserstein distance for sets of measures and links it to the weak convergence of sublinear expectations, providing a novel theoretical tool.

Findings

Generalized Wasserstein distance effectively characterizes weak convergence.

The framework extends classical Wasserstein concepts to sublinear expectations.

Provides a new approach for analyzing convergence in uncertain probability models.

Abstract

In this paper, we define the generalized Wasserstein distance for sets of Borel probability measures and demonstrate that the weak convergence of sublinear expectations can be characterized by means of this distance.