Maximal irreducibility measure for spatial birth-and-death processes

TL;DR

This paper establishes that, under broad conditions, the Lebesgue-Poisson measure serves as the maximal irreducibility measure for spatial birth-and-death processes, enhancing understanding of their probabilistic structure.

Contribution

It proves that the Lebesgue-Poisson measure is the maximal irreducibility measure for spatial birth-and-death processes under general conditions.

Findings

Lebesgue-Poisson measure is maximal irreducibility measure

Results apply under broad conditions on birth and death rates

Advances understanding of spatial birth-and-death process structure

Abstract

We prove that under certain general conditions on the birth and death rates the Lebesgue-Poisson measure is a maximal irreducibility measure for the spatial birth-and-death process.