Geodesic
On the strong convergence of the sequence of diffusion type processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 866-872 
S. I. Pisanec. On the strong convergence of the sequence of diffusion type processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 866-872. http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a19/
@article{TVP_1979_24_4_a19,
     author = {S. I. Pisanec},
     title = {On the strong convergence of the sequence of diffusion type processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {866--872},
     year = {1979},
     volume = {24},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a19/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\xi_t^{(n)}$, $t\le T$ be the sequence of solutions of stochastic differential equations $$ d\xi_t^{(n)}=\alpha_t^{(n)}(\xi_t^{(n)})\,dt+dw_t,\qquad\xi_t^{(n)}=0,\qquad n=0,1,\dots $$ In this paper we study the conditions under which $$ \lim_{n\to\infty}\mathbf M\biggl|\int_0^t\alpha_s^{(n)}(w)\,ds- \int_0^t\alpha_s^{(0)}(w)\,ds\biggr|^2=0,\qquad t\le T, $$ and the conditions under which $$ \lim_{n\to\infty}\mathbf M|\xi_t^{(n)}-\xi_t^{(0)}|^2=0,\qquad t\le T. $$