Nonlinear branching processes with immigration

TL;DR

This paper constructs nonlinear branching processes with immigration using stochastic integral equations driven by Poisson measures and establishes criteria for their regularity, recurrence, and ergodic properties.

Contribution

It introduces a novel construction of nonlinear branching processes with immigration and provides new criteria for their long-term behavior.

Findings

Criteria for regularity and recurrence established

Conditions for ergodicity and strong ergodicity derived

Process constructed as unique solution to stochastic integral equation

Abstract

The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson ran- dom measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.