Geodesic
On stochastic differential equations with boundary conditions in a~half-plane
Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 423-437

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Existence theorems are proved for solutions of stochastic differential equations with boundary conditions in a Euclidean half-space. The existence of Markov processes with given characteristics in a half-space is deduced from these theorems. The case of discontinuous coefficients is included. The usual nondegeneracy condition for the normal component of diffusion near the boundary is replaced in part by the nondegeneracy of the jump component. Bibliography: 15 titles. 
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     author = {S. V. Anulova},
     title = {On stochastic differential equations with boundary conditions in a~half-plane},
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S. V. Anulova. On stochastic differential equations with boundary conditions in a~half-plane. Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 423-437. http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a1/