On quasi-diffusional processes

In the paper a Markov process $X$ in an Euclidean space is constructed for each elliptic differential operator $L$ of the second order with a continuous principal part. We prove that $X$ is a quasi-diffusional process with the oorreisponding differential operator equal to $L$. The infinitesimal operator of the part of $X$ in a domain with a fimooth, boundary is completely discribed in terms of Sobolev's spaces.