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

G. V. Riabov

01004, Ukraine, Kiev–4, 3, Tereschenkivska st.

Аннотация: 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.

Ключевые слова: Gaussian measure, extended stochastic integral, optimal transport.

MSC: Primary 60G15; Secondary 60H07

Язык публикации: английский

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