Backbone decomposition for continuous-state branching processes with immigration

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: MSC: 60J80 60E10 Keywords: Backbone decomposition N-measure Continuous state branching process with immigration a b s t r a c t In the spirit of Duquesne 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 equivalent in law to a continuous-time Galton–Watson process with immigration (with Poissonian dressing). The result also helps to characterise the limiting backbone decomposition which is predictable from the work on consistent growth of Galton–Watson trees with immigration in Cao and Winkel (2010).