Changing the branching mechanism of a continuous state branching process using immigration

Romain Abraham (1) , Jean-François Delmas (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We construct a continuous state branching process with immigration (CBI) whose immigration depends on the CBI itself and we recover a continuous state branching process (CB). This provides a dual construction of the pruning at nodes of CB introduced by the authors in a previous paper. This construction is a natural way to model neutral mutation. Using exponential formula, we compute the probability of extinction of the original type population in a critical or sub-critical quadratic branching, conditionally on the non extinction of the total population.

Domaines: Probabilités [math.PR]

Romain Abraham, Jean-François Delmas. Changing the branching mechanism of a continuous state branching process using immigration. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2009, 45 (1), pp.226-238. ⟨10.1214/07-AIHP165⟩. ⟨hal-00096275v2⟩