Fragmentation at height associated to Lévy processes

Details Fragmentation at height associated to Lévy processes Fragmentation at height associated to Lévy processes

2006-03-08

arxiv.org/abs/math/0603193v1

Stochastic processes and their applications 117 (2007) 297-311

Mathematics

Probability

Scientific paper

We consider the height process of a L\'{e}vy process with no negative jumps, and its associated continuous tree representation. Using tools developed by Duquesne and Le Gall, we construct a fragmentation process at height, which generalizes the fragmentation at height of stable trees given by Miermont. In this more general framework, we recover that the dislocation measures are the same as the dislocation measures of the fragmentation at node introduced by Abraham and Delmas, up to a factor equal to the fragment size. We also compute the asymptotic for the number of small fragments.

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