Geodesic
A functional central limit theorem for semimartingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 683-703 
R. Š. Lipčer; A. N. Širyaev. A functional central limit theorem for semimartingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 683-703. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a1/
@article{TVP_1980_25_4_a1,
     author = {R. \v{S}. Lip\v{c}er and A. N. \v{S}iryaev},
     title = {A functional central limit theorem for semimartingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {683--703},
     year = {1980},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X^n$, $n\geqslant 1$, be a sequence of semimartingales with triplets of local characteristics $T^n=(B^n,\langle X^{cn}\rangle,\nu^n)$ and let $X$ be a continuous Gaussian martingale with a triplet $T=(0,\langle X\rangle,0)$. We give conditions on the convergence of the triplets $T^n$ to $T$ which are sufficient for the weak convergence of the distributions of $X^n$ to the distribution of $X$ and for the weak convergence of the finite-dimensional distributions of $X^n$ to the corresponding finite-dimensional distributions of $X$.