Geodesic
On the rate of convergence in the central limit theorem for semimartingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 3-14

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Let $(X^n)_{n\ge 1}$ be a family of semimartingales with the canonical representation (1). Under the conditions (А), (В), (C) the central limit theorem is valid: $$ R_t^n=\sup_x\biggl|\mathbf P\{X_t^n\le x\}-\Phi\biggl(\frac{x}{\sqrt V_t}\biggr)\biggr|\to0,\qquad n\to\infty. $$ We give the estimates (3)–(6) for the rate of convergence of $R_t^n$ in the cases when $(X^n)_{n\ge 1}$ are families of semimartingales, local martingales and local square integrable martingales. 
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     author = {R. \v{S}. Lip{\cyrs}er and A. N. \v{S}iryaev},
     title = {On the rate of convergence in the central limit theorem for semimartingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
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     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a0/}
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R. Š. Lipсer; A. N. Širyaev. On the rate of convergence in the central limit theorem for semimartingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a0/