Geodesic
A representation for the Kantorovich--Rubinstein distance defined by the Cameron--Martin norm of a Gaussian measure on a Banach space
Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 84-90

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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.
Keywords: Gaussian measure, extended stochastic integral
Mots-clés : optimal transport. 
@article{THSP_2016_21_2_a6,
     author = {G. V. Riabov},
     title = {A representation for the {Kantorovich--Rubinstein} distance defined by the {Cameron--Martin} norm of a {Gaussian} measure on a {Banach} space},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {84--90},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a6/}
}
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G. V. Riabov. A representation for the Kantorovich--Rubinstein distance defined by the Cameron--Martin norm of a Gaussian measure on a Banach space. Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 84-90. http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a6/