Geodesic
On the existence of a~strong solution of an Ito stochastic differential equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 120-123

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It is shown that the scalar stochastic differential equation $$ x_t=x_0+\int_0^t A(s,x_s)\,ds+\int_0^t B(s,x_s)\,dw_s,\qquad 0\le t\le T, $$ has at least one strong solution under the following conditions: a) scalar functions $A(t,x)$ and $B(t,x)$ are continuous in both $t$, $x$ for $0\le t\le T$, $-\infty$; b) $B(t,x)$ satisfies a local Lipschitz conditions in $x$; c) $|A(t,x)|+ |B(t,x)|\le L(1+|x|)$ for some constant $L$ and all $t$, $x$; d) $\mathbf Mx_0^2\infty$. 
@article{TVP_1984_29_1_a11,
     author = {I. V. Fedorenko},
     title = {On the existence of a~strong solution of an {Ito} stochastic differential equation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {120--123},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a11/}
}
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I. V. Fedorenko. On the existence of a~strong solution of an Ito stochastic differential equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 120-123. http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a11/