Volume 15, 2011
|Page(s)||372 - 389|
|Published online||05 January 2012|
Dislocation measure of the fragmentation of a general Lévy tree
MAPMO CNRS UMR 6628,
Fédération Denis Poisson 2964,
45067 Orléans Cedex 2
Revised: 9 November 2009
Revised: 22 January 2010
Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab. 7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th. Rel. Fiel 141 (2008) 113–154].
Mathematics Subject Classification: 60J25 / 60G57 / 60J80
Key words: Fragmentation / Lévy CRT
© EDP Sciences, SMAI, 2011
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