Poisson Snake and Fragmentation
Romain Abraham, Université René Descartes (Paris 5)
Laurent Serlet, Université René Descartes (Paris 5)
Abstract
Our main object that we call the Poisson snake is a Brownian snake as
introduced by Le Gall. This process has values which are trajectories
of standard Poisson process stopped at some random finite lifetime
with Brownian evolution.
We use this
Poisson snake to construct a self-similar fragmentation as
introduced by Bertoin. A similar representation was given by
Aldous and Pitman using the Continuum Random Tree.
Whereas their proofs used
approximation by discrete models, our representation allows
continuous time arguments.
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