An improved multivariate version of Kolmogorov's second uniform limit theorem

TL;DR

This paper extends previous results on approximating distributions of sums of independent variables by infinitely divisible laws to the context of convex polyhedra, enhancing the understanding of distributional closeness in multivariate settings.

Contribution

It introduces a multivariate version of Kolmogorov's second uniform limit theorem, applying it to convex polyhedra for improved distribution approximation.

Findings

Extended approximation results to convex polyhedra

Demonstrated transferability of earlier univariate results

Enhanced multivariate distribution approximation techniques

Abstract

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be transferred to the estimation of the closeness of distributions on convex polyhedra.