Fragmentation associated to Levy processes using snake

Romain Abraham; Jean-Francois Delmas

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Fragmentation associated to Levy processes using snake

Romain Abraham·Jean-Francois Delmas

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Abstract

We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Duquesne and Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is interesting in itself.

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Romain Abraham, Jean-Francois Delmas. 2005-11-29. Fragmentation associated to Levy processes using snake. https://arxiv.org/abs/math/0511702

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