HAL: hal-00015553, version 1

arXiv: math.PR/0512195

DOI: 10.1007/s10959-007-0082-1

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Journal of Theoretical Probability 20 (2007) 355-370

Feller property and infinitesimal generator of the exploration process

Romain Abraham 1, Jean-François Delmas 2

(2007)

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.

1:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
2:	Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
	INRIA – Ecole des Ponts ParisTech

Subject

:

Mathematics/Probability

Keyword(s): Exploration process – Levy snake – Feller property – measure-valued process – infinitesimal generator

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From: Romain Abraham <>

Submitted on: Friday, 9 December 2005 13:08:10

Updated on: Thursday, 7 June 2007 10:48:31