A moment approach to the law of large numbers for supercritical branching Markov processes

TL;DR

This paper introduces a new proof for the law of large numbers in supercritical branching Markov processes, utilizing moment asymptotics, and demonstrates that the limit distribution is fully characterized by its moments.

Contribution

It provides a novel moment-based proof of the law of large numbers and establishes that the limit distribution is uniquely determined by its moments.

Findings

New proof of the law of large numbers for branching Markov processes

The limiting distribution is uniquely determined by its moments

Utilizes asymptotic behavior of moments from previous work

Abstract

We offer a new proof of the classical law of large numbers for a general class of branching Markov processes based on the asymptotic behaviour of the moments developed in \cite{bmoments, gonzalez2022erratum}. Moreover, we show that the law of the limiting random variable, that is the almost sure limit of the classical additive martingale, is completely determined by its moments.