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Fragmentation associated with Levy processes using snake

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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Submitted on : Wednesday, March 7, 2007 - 1:34:35 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
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Romain Abraham, Jean-François Delmas. Fragmentation associated with Levy processes using snake. Probability Theory and Related Fields, Springer Verlag, 2008, 141, pp.113-154. ⟨10.1007/s00440-007-0081-2⟩. ⟨hal-00014673v2⟩

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