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Dislocation measure of the fragmentationof a general Lévy tree

Published online by Cambridge University Press:  05 January 2012

Guillaume Voisin
Guillaume Voisin*
Affiliation:
MAPMO CNRS UMR 6628, Fédération Denis Poisson 2964, Université d'Orléans, B.P. 6759, 45067 Orléans Cedex 2 France; guillaume.voisin@uni-due.de
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Abstract

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].

Keywords

FragmentationLévy CRT
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 372 - 389
Copyright
© EDP Sciences, SMAI, 2011

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References

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