Backbone decomposition for continuous-state branching processes with immigration

TL;DR

This paper establishes a backbone decomposition for supercritical continuous-state branching processes with immigration, linking them to Galton-Watson processes with immigration and Poissonian dressing, extending previous theoretical frameworks.

Contribution

It introduces a novel backbone decomposition for these processes, generalizing prior models and connecting continuous-state processes with discrete Galton-Watson processes.

Findings

Backbone decomposition characterized for supercritical processes

Connection established between continuous-state and Galton-Watson processes

Predictable limiting backbone structure derived

Abstract

In the spirit of Duqesne and Winkel (2007) and Berestycki et al. (2011) we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equal in law to a continuous-time Galton Watson process with immigration with Poissonian dressing. The result also characterises the limiting backbone decomposition which is predictable from the work on consistent growth of Galton-Watson trees with immigration in Cao and Winkel (2010).