Geodesic
A~local limit theorem on the convergence to a~diffusion
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 591-597

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We give sufficient conditions for the validity of the local limit theorem for the convergence of a sequence of homogeneous Markov chains to a diffusion process. 
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     author = {A. N. Konovalov},
     title = {A~local limit theorem on the convergence to a~diffusion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {591--597},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a11/}
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A. N. Konovalov. A~local limit theorem on the convergence to a~diffusion. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 591-597. http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a11/