Height process for super-critical continuous state branching process
Probability
2007-05-23 v1
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 give a complete duality picture between pruning and size proportional immigration for quadratic continuous state branching processes.
Cite
@article{arxiv.math/0611172,
title = {Height process for super-critical continuous state branching process},
author = {Jean-François Delmas},
journal= {arXiv preprint arXiv:math/0611172},
year = {2007}
}