Geodesic
On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 685-701

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We investigate the sufficient conditions for the strong and weak uniqueness of the solution of a stochastic equation with a simultaneous reflection at zero: \begin{gather*} dx_s=\sigma(s,x_s)\,dw_s+b(s,x_s)\,ds+d\varphi_s, \\ d\varphi_s=\chi_{x_s=0}\,d\varphi_s,\qquad x_s\ge 0, \end{gather*} and for the existence of a strong solution of this equation. 
@article{TVP_1981_26_4_a1,
     author = {A. Ju. Veretennikov},
     title = {On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {685--701},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/}
}
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A. Ju. Veretennikov. On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 685-701. http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/