Height Process for Super-critical Continuous State Branching Process

#### J.-F. Delmas

2008, v.14, Issue 2, 309-326

ABSTRACT

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 gives a complete duality picture between pruning and size proportional immigration for quadratic continuous state branching processes.

Keywords: Brownian snake,branching process,height process,Ray-Knight theorem,local time,reflected Brownian motion,Brownian motion with drift