Abstract
We prove that, for the distributions of one-dimensional diffusions with nonconstant diffusion coefficients, the Monge and Kantorovich problems associated with the cost function generated by the Cameron-Martin norm have no nontrivial solutions, i.e., are solvable only when the considered measures coincide. In particular, this is true if the diffusion coefficient is real-analytic and nonconstant.
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Bukin, D.B. On the Monge and Kantorovich problems for distributions of diffusion processes. Math Notes 96, 864–870 (2014). https://doi.org/10.1134/S0001434614110236
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DOI: https://doi.org/10.1134/S0001434614110236