Geodesic
On the strong solutions of stochastic differential equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 2, pp. 348-360

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It is proved that under some conditions the equation $$ x_t=x_0+\int_0^t\sigma(s,x_s)\,dw_s+\int_0^t b(s,x_s)\,ds $$ has a strong solution and that the pathwise uniqueness for this solution holds. 
@article{TVP_1979_24_2_a7,
     author = {A. Yu. Veretennikov},
     title = {On the strong solutions of stochastic differential equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {348--360},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_2_a7/}
}
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A. Yu. Veretennikov. On the strong solutions of stochastic differential equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 2, pp. 348-360. http://geodesic.mathdoc.fr/item/TVP_1979_24_2_a7/