Electronic Journal of Probability
- Electron. J. Probab.
- Volume 7 (2002), paper no. 17, 15 pp.
Poisson Snake and Fragmentation
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.
Electron. J. Probab. Volume 7 (2002), paper no. 17, 15 pp.
Accepted: 1 July 2002
First available in Project Euclid: 16 May 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G57: Random measures
This work is licensed under a Creative Commons Attribution 3.0 License.
Abraham, Romain; Serlet, Laurent. Poisson Snake and Fragmentation. Electron. J. Probab. 7 (2002), paper no. 17, 15 pp. doi:10.1214/EJP.v7-116. https://projecteuclid.org/euclid.ejp/1463434890