A representation for the Kantorovich–Rubinstein distance defined by the Cameron–Martin norm of a Gaussian measure on a Banach space

A representation for the Kantorovich–Rubinstein distance between probability measures on a separable Banach space $X$ in the case when this distance is defined by the Cameron–Martin norm of a centered Gaussian measure $\mu$ on $X$ is obtained in terms of the extended stochastic integral (or divergence) operator.