Height process for super-critical continuous state branching process

Jean-François Delmas (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity. Then we extend the pruning procedure of branching processes to the super-critical case. This give a complete duality picture between pruning and size proportional immigration for quadratic continuous state branching processes.

Mots clés: Brownian snake; branching process; height process; Ray-Knight theorem; local time; reflected Brownian motion; Brownian motion with drift

Domaines: Probabilités [math.PR]

Jean-François Delmas. Height process for super-critical continuous state branching process. 2006. ⟨hal-00112029⟩