On Alternative Approximating Distributions in the Multivariate Version of Kolmogorov's Second Uniform Limit Theorem

Abstract

The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of approximating infinitely divisible distributions. We will also generalize the results to the infinite-dimensional case.