On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem

TL;DR

This paper explores alternative infinitely divisible distributions for approximating sums of independent variables, extending previous results to convex polyhedra and infinite-dimensional spaces.

Contribution

It introduces an alternative class of infinitely divisible distributions for approximation and generalizes the results to infinite-dimensional settings.

Findings

Alternative distributions effectively approximate sums of independent variables.

Results extend to convex polyhedra and infinite-dimensional spaces.

Provides a new approach to distribution approximation in probability theory.

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.