A limit theorem for occupation measures of L\'evy processes in compact groups

TL;DR

This paper provides a concise proof of a condition under which the normalized occupation measure of a Lévy process in a compact group converges to a uniform distribution almost surely.

Contribution

It establishes a necessary and sufficient condition for the asymptotic uniformity of occupation measures of Lévy processes in compact groups.

Findings

Condition for asymptotic uniformity proved

Normalized occupation measure converges to uniform distribution

Provides a short, elegant proof

Abstract

A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a L\'evy process in a metrizable compact group to be asymptotically uniform with probability one.