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Fragmentation associated with Lévy processes using snake.
- Source :
- Probability Theory & Related Fields; May2008, Vol. 141 Issue 1/2, p113-154, 42p, 3 Graphs
- Publication Year :
- 2008
-
Abstract
- We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-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 of its own interest. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01788051
- Volume :
- 141
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Probability Theory & Related Fields
- Publication Type :
- Academic Journal
- Accession number :
- 28716128
- Full Text :
- https://doi.org/10.1007/s00440-007-0081-2