| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 372 - 389 | |
| DOI | https://doi.org/10.1051/ps/2010006 | |
| Published online | 05 January 2012 | |
Dislocation measure of the fragmentation of a general Lévy tree
MAPMO CNRS UMR 6628,
Fédération Denis Poisson 2964,
Université d'Orléans,
B.P. 6759,
45067 Orléans Cedex 2
France; guillaume.voisin@uni-due.de
Received:
23
March
2009
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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