ИСТИНА

We consider the Monge and Kantorovich problems associated with the cost function generated by the Cameron--Martin norm for nonlinear images of the Wiener measure, i.e., for the distributions of one-dimensional diffusions with nonconstant diffusion coefficients. In this case these problems fail to have nontrivial solutions. In particular, this is true if the diffusion coefficient is real-analytic and nonconstant.