Geodesic
Stochastic differential equations depending on a parameter
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 675-682 
A. V. Skorohod. Stochastic differential equations depending on a parameter. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 675-682. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a0/
@article{TVP_1980_25_4_a0,
     author = {A. V. Skorohod},
     title = {Stochastic differential equations depending on a~parameter},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {675--682},
     year = {1980},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a stochastic differential equation $$ d\xi_\theta=a_\theta(t,\xi_\theta(\,\cdot\,))\,dt+B_\theta(t,\xi_\theta(t))\,dw(t),\qquad\xi_\theta(0)=x_\theta, $$ such that its coefficients and initial condition are continuous functions of $\theta\in\Theta$, where $\Theta$ is a complete metric space. If an equation has a strong solution on a dense subset $\Theta_1\subset\Theta$, then $\Theta_1$ is of the second category and coincides with the set $\Theta_0$ of continuity of $\xi_\theta(t)$.