Geodesic
On strong solutions and explicit formulas for solutions of stochastic integral equations
Sbornik. Mathematics, Tome 39 (1981) no. 3, pp. 387-403

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Conditions are obtained under which the stochastic equation $$ x_t=x+\int^t_0\sigma(s,x_s)\,dw_s+\int^t_0b(s,x_s)\,ds $$ has a strong solution. In particular, in the multidimensional case where the diffusion matrix $\sigma$ is the identity matrix and the drift vector $b$ is bounded, these conditions are satisfied. Bibliography: 13 titles. 
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     author = {A. Yu. Veretennikov},
     title = {On strong solutions and explicit formulas for solutions of stochastic integral equations},
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A. Yu. Veretennikov. On strong solutions and explicit formulas for solutions of stochastic integral equations. Sbornik. Mathematics, Tome 39 (1981) no. 3, pp. 387-403. http://geodesic.mathdoc.fr/item/SM_1981_39_3_a4/