Geodesic
On small perturbations of coefficients of a~diffusion process
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 536-540

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It is proved that the sample paths of a diffusion process converge in probability uniformly provided that the coefficients $b_i(x)$ in (1) converge in the weak sense. Hence follow some theorems on Dirichlet problem solutions. 
@article{TVP_1967_12_3_a11,
     author = {M. I. Freidlin},
     title = {On small perturbations of coefficients of a~diffusion process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {536--540},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a11/}
}
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M. I. Freidlin. On small perturbations of coefficients of a~diffusion process. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 536-540. http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a11/