This article is cited in 26 papers

On quasi-diffusional processes

N. V. Krylov

Moscow

Abstract: 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.

Received: 17.04.1965

 English version: Theory of Probability and its Applications, 1966, 11:3, 373–389

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