Geodesic
On the strong solutions of stochastic differential equations with nonsmooth coefficients
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 146-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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By means of purely probabilistic methods we prove the existence of strong solution of a stochastic differential equation $$ dx(t,\omega)=f(x(t,\omega))\,dt+dw(t,\omega),x(0,\omega)=x_0\in R^1,\ 0\le t\le T<\infty, $$ in the case when the drift coefficient $f(x)$ is bounded and piecewise smooth or continuous function. 
@article{TVP_1979_24_1_a10,
     author = {A. V. Mel'nikov},
     title = {On the strong solutions of stochastic differential equations with nonsmooth coefficients},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {146--149},
     year = {1979},
     volume = {24},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/}
}
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A. V. Mel'nikov. On the strong solutions of stochastic differential equations with nonsmooth coefficients. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 146-149. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/