On the Kantorovich problem for nonlinear images of the Wiener measure

Resumo

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.