Electronic Journal of Probability

Poisson Snake and Fragmentation

Romain Abraham and Laurent Serlet

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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.

Article information

Electron. J. Probab. Volume 7 (2002), paper no. 17, 15 pp.

Accepted: 1 July 2002
First available in Project Euclid: 16 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Path-valued process Brownian snake Poisson process fragmentation coalescence self-similarity

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

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