Geodesic
Generalization and refinement of the integro-local Stone theorem for sums of random vectors
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 659-685

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The integro-local Stone theorem on the asymptotics of the probability that a sum of random vectors enters a small cube is (a) refined under additional moment and structural conditions; (b) generalized to a case of nonidentically distributed summands in the triangular array scheme; (c) the results of item (b) are refined under additional moment and structural conditions.
Keywords: integro-local Stone theorem, sums of random vectors, bound for the remainder term, triangular array scheme. 
@article{TVP_2016_61_4_a2,
     author = {A. A. Borovkov},
     title = {Generalization and refinement of the integro-local {Stone} theorem for sums of random vectors},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {659--685},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a2/}
}
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A. A. Borovkov. Generalization and refinement of the integro-local Stone theorem for sums of random vectors. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 659-685. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a2/