Dislocation measure of the fragmentation of a general Lévy tree

Guillaume Voisin

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page 372-389
  • ISSN: 1292-8100

Abstract

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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].

How to cite

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Voisin, Guillaume. "Dislocation measure of the fragmentation of a general Lévy tree." ESAIM: Probability and Statistics 15 (2011): 372-389. <http://eudml.org/doc/277161>.

@article{Voisin2011,
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].},
author = {Voisin, Guillaume},
journal = {ESAIM: Probability and Statistics},
keywords = {fragmentation; Lévy CRT},
language = {eng},
pages = {372-389},
publisher = {EDP-Sciences},
title = {Dislocation measure of the fragmentation of a general Lévy tree},
url = {http://eudml.org/doc/277161},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Voisin, Guillaume
TI - Dislocation measure of the fragmentation of a general Lévy tree
JO - ESAIM: Probability and Statistics
PY - 2011
PB - EDP-Sciences
VL - 15
SP - 372
EP - 389
AB - 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].
LA - eng
KW - fragmentation; Lévy CRT
UR - http://eudml.org/doc/277161
ER -

References

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  2. [2] R. Abraham, J.-F. Delmas and G. Voisin, Pruning a Lévy random continuum tree. preprint Zbl1231.60073
  3. [3] R. Abraham and L. Serlet, Poisson snake and fragmentation. Elect. J. Probab.7 (2002) 1–15. Zbl1015.60046MR1943890
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