Journal of Theoretical Probability

, Volume 20, Issue 2, pp 355–370 | Cite as

Feller Property and Infinitesimal Generator of the Exploration Process

  • Romain AbrahamEmail author
  • Jean-François Delmas


We consider the exploration process associated to the continuous random tree (CRT) built using a Lévy 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.


Exploration process Lévy snake Feller property Measure valued process Infinitesimal generator 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.MAPMO, Université d’OrléansOrleans cedex 2France
  2. 2.ENPC-CERMICSMarne La ValleeFrance

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