Construction of age-structured branching processes by stochastic equations

TL;DR

This paper develops stochastic integral equation methods to construct age-structured branching processes, providing conditions for ergodicity with immigration, advancing mathematical understanding of these models.

Contribution

It introduces a novel stochastic integral equation framework for constructing age-structured branching processes, including criteria for ergodicity with immigration.

Findings

Established pathwise unique solutions for the processes.

Derived necessary and sufficient conditions for ergodicity.

Enhanced mathematical tools for analyzing age-structured models.

Abstract

We give constructions of age-structured branching processes without or with immigration as pathwise unique solutions to stochastic integral equations. A necessary and sufficient condition for the ergodicity of the model with immigration is also given.