Geodesic
On criteria for the existence of the strong solution of the stochastic equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 417-424

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Criteria for the existence of the strong solution and for the strong uniqueness of a solution of the Ito's stochastic differential equation $$ dx_t=\sigma(t,x_t)\,dw_t+b(t,x_t)\,dt,\qquad x_0=x\in E_d, $$ are formulated in terms of the linear parabolic equations theory and proved. 
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     author = {A. Yu. Veretennikov},
     title = {On criteria for the existence of the strong solution of the stochastic equation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {417--424},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a0/}
}
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A. Yu. Veretennikov. On criteria for the existence of the strong solution of the stochastic equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 417-424. http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a0/