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Certain class of nonuniform estimates in multidimensional limit theorems

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Abstract

Quantities of the form | F(X) — G(X) | are estimated, where F and G are the convolutions of certain k-dimensional probability distributions, while X is a convex polyhedron in Rk. Estimates of the form | F(X) — G(X) | ≤ c(k)εβ(F, G, X) are proved, differing from the known ones by the presence of the factor β(F, G, X) in the right-hand side, which may turn out to be small if the polyhedron X is small in a definite sense.

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Authors
  1. A. Yu. Zaitsev
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 92–105, 1990.

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Zaitsev, A.Y. Certain class of nonuniform estimates in multidimensional limit theorems. J Math Sci 68, 459–468 (1994). https://doi.org/10.1007/BF01254270

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  • DOI: https://doi.org/10.1007/BF01254270

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