Geodesic
On processes with L\'evy generating operator in a~half-space
Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 9-51

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The author considers a stochastic differential equation in a half-space with boundary conditions of Ventcel'. Under mild regularity conditions imposed on the coefficients the existence of a solution is proved, and the Markov property thereof is studied. From the results the existence of a Markov process in a half-space, with corresponding generating operator and boundary conditions, is deduced. An ancillary estimate of the distribution density of a stochastic integral, which is of independent interest, is also proved. Bibliography: 20 titles. 
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     title = {On processes with {L\'evy} generating operator in a~half-space},
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S. V. Anulova. On processes with L\'evy generating operator in a~half-space. Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 9-51. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a1/