Electronic Journal of Probability

Poisson Snake and Fragmentation

Romain Abraham and Laurent Serlet

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1463434890

Digital Object Identifier
doi:10.1214/EJP.v7-116

Mathematical Reviews number (MathSciNet)
MR1943890

Zentralblatt MATH identifier
1015.60046

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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