On constructing a multidimensional diffusion process with a membrane located on a given hyperplane and acting in an oblique direction

Using the methods of the theory of classical potentials, we have constructed a Feller semigroup of linear operators that generates a multidimensional diffusion process whose diffusion matrix is given by a sufficiently regular function and whose drift vector is given by a generalized function of the type of a δ - function concentrated on a given hyperplane. Such process can serve as a mathematical model for describing the motion of a diffusing particle in a medium where a membrane is located on the hyperplane. The particle is receiving "a pulse of infinite intensity" at those instants of time when it is hitting the hyperplane. The direction of those pulses are determined by a vector field given on that hyperplane. It is important to emphasize that the trajectories of the process constructed are continuous.