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Article Dans Une Revue Stochastic Processes and their Applications Année : 2007

Fragmentation at height associated to Lévy processes

Résumé

We consider the height process of a Lévy 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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Dates et versions

hal-00020271 , version 1 (08-03-2006)

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Jean-François Delmas. Fragmentation at height associated to Lévy processes. Stochastic Processes and their Applications, 2007, 117 (3), pp.297-311. ⟨hal-00020271⟩
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