Feller property and infinitesimal generator of the exploration process

Romain Abraham; Jean-Francois Delmas

doi:10.1007/s10959-007-0082-1

paper

Feller property and infinitesimal generator of the exploration process

arXiv:math/0512195 · doi:10.1007/s10959-007-0082-1

Abstract

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.