Diffusion processes with generalized drift vector

Continuous Markov processes in $R^{m}$ are constructed or which the diffusion coefficients exist in a generalized sense. These generalized coefficients are: a non-singular Hölder continuous diffusion matrix and a drift vector which is represented in the form $a(x)=\overline N(x)\delta_S(x)$ where $S$ is a $(m-1)$-dimensional surface, $\overline N(x)$ is a vector field and $\delta_S(x)$ is a generalized function the action of which onto basic functions is reduced to integration over $S$.