Convergence to infinite-dimensional compound Poisson distributions on convex polyhedra

TL;DR

This paper extends previous results on approximating sums of independent random variables by compound Poisson distributions from finite to infinite-dimensional spaces, focusing on convex polyhedra.

Contribution

It demonstrates that approximation techniques and proximity estimates for multidimensional distributions can be almost automatically adapted to infinite-dimensional settings.

Findings

Approximation methods transfer to infinite-dimensional spaces.

Estimates of distribution proximity remain valid in infinite dimensions.

Results apply to convex polyhedra in infinite-dimensional spaces.

Abstract

The aim of the present work is to provide a supplement to the authors' paper (2018). It is shown that our results on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential convolutions of multidimensional distributions on convex polyhedra may be almost automatically transferred to the infinite-dimensional case.