Poisson snake and fragmentation. (English) Zbl 1015.60046

Abraham, R.; Serlet, L.

Electron. J. Probab. 7, Paper No. 17, 15 p. (2002).

Authors’ 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.

Reviewer: Thomas Simon (Évry)

MSC:

60G57	Random measures
60J25	Continuous-time Markov processes on general state spaces

Keywords:

path-valued process; Brownian snake; Poisson process; fragmentation; coalescence; self-similarity critical probability; percolation