Feller Property and Infinitesimal Generator of the Exploration Process
- 66 Downloads
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.
KeywordsExploration process Lévy snake Feller property Measure valued process Infinitesimal generator
Unable to display preview. Download preview PDF.
- 1.Abraham, R., Delmas, J.-F.: Fragmentation associated with Lévy processes using snake. Preprint CERMICS (2005) Google Scholar
- 4.Duquesne, T., Le Gall, J.-F.: Random trees, Lévy processes and spatial branching processes. Astérisque 281 (2002) Google Scholar
- 8.Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion, 2nd edn. Springer, New York (1995) Google Scholar