Feller property and infinitesimal generator of the exploration process

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 consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale.

Mots clés: Exploration process; Levy snake; Feller property; measure-valued process; infinitesimal generator

Domaines: Probabilités [math.PR]

Romain Abraham, Jean-François Delmas. Feller property and infinitesimal generator of the exploration process. Journal of Theoretical Probability, 2007, 20, pp.355-370. ⟨10.1007/s10959-007-0082-1⟩. ⟨hal-00015553⟩