This article is cited in 17 papers

Diffusion processes with generalized drift vector

N. I. Portenko

Kiev

Abstract: 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 $S$.

Received: 30.05.1977

 English version: Theory of Probability and its Applications, 1979, 24:1, 62–77

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