A representation for the Kantorovich--Rubinstein distance on the abstract Wiener space
Georgii Riabov
TL;DR
This paper presents a new way to represent the Kantorovich--Rubinstein distance between probability measures on an abstract Wiener space using the extended stochastic integral operator.
Contribution
It introduces a novel representation of the Kantorovich--Rubinstein distance leveraging the extended stochastic integral in an abstract Wiener space.
Findings
Provides a new integral representation of the distance
Connects optimal transport with stochastic calculus
Enhances understanding of probability measures on Wiener spaces
Abstract
A representation for the Kantorovich--Rubinstein distance between probability measures on an abstract Wiener space in terms of the extended stochastic integral (or, divergence) operator is obtained.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Point processes and geometric inequalities · advanced mathematical theories