Feller property and infinitesimal generator of the exploration process

Details Feller property and infinitesimal generator of the exploration process Feller property and infinitesimal generator of the exploration process

2005-12-09

arxiv.org/abs/math/0512195v1

Journal of Theoretical Probability 20 (2007) 355-370

Mathematics

Probability

Scientific paper

10.1007/s10959-007-0082-1

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.

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