Geodesic
On the Kantorovich Problem for Nonlinear Images of the Wiener Measure
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 682-688

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The Kantorovich problem with the cost function given by the Cameron–Martin norm is considered for nonlinear images of the Wiener measure that are distributions of one-dimensional diffusion processes with nonconstant diffusion coefficients. It is shown that the problem can have trivial solutions only if the derivative of the diffusion coefficient differs from zero almost everywhere.
Keywords: Kantorovich problem, Wiener measure.
Mots-clés : distribution of a diffusion process, Cameron–Martin space 
@article{MZM_2016_100_5_a3,
     author = {D. B. Bukin},
     title = {On the {Kantorovich} {Problem} for {Nonlinear} {Images} of the {Wiener} {Measure}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {682--688},
     publisher = {mathdoc},
     volume = {100},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a3/}
}
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D. B. Bukin. On the Kantorovich Problem for Nonlinear Images of the Wiener Measure. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 682-688. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a3/