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].
@article{PS_2011__15__372_0, author = {Voisin, Guillaume}, title = {Dislocation measure of the fragmentation of a general {L\'evy} tree}, journal = {ESAIM: Probability and Statistics}, pages = {372--389}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2010006}, mrnumber = {2870521}, zbl = {1263.60068}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2010006/} }
TY - JOUR AU - Voisin, Guillaume TI - Dislocation measure of the fragmentation of a general Lévy tree JO - ESAIM: Probability and Statistics PY - 2011 SP - 372 EP - 389 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2010006/ DO - 10.1051/ps/2010006 LA - en ID - PS_2011__15__372_0 ER -
Voisin, Guillaume. Dislocation measure of the fragmentation of a general Lévy tree. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 372-389. doi : 10.1051/ps/2010006. http://www.numdam.org/articles/10.1051/ps/2010006/
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