Geodesic
Necessary and sufficient conditions for the functional central limit theorem for semimartingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 1, pp. 132-137

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Suppose that $X^n$, $n\ge 1$, is a family of semimartingales with the triplets of local characteristics $(B^n,\langle X^{nc}\rangle,\nu^n)$ and $M$ is a continuous Gaussian martingale. We find conditions which are necessary and sufficient for the weak convergence $X^n\overset{\mathscr D}{\to}M$ ($n\to\infty$). 
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     author = {R. \v{S}. Lipcer and A. N. \v{S}iryaev},
     title = {Necessary and sufficient conditions for the functional central limit theorem for semimartingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {132--137},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/}
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R. Š. Lipcer; A. N. Širyaev. Necessary and sufficient conditions for the functional central limit theorem for semimartingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 1, pp. 132-137. http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/