Electronic Journal of Probability

Ordered Additive Coalescent and Fragmentations Associated to Lévy Processes with No Positive Jumps

Grégory Miermont

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Abstract

We study here the fragmentation processes that can be derived from Lévy processes with no positive jumps in the same manner as in the case of a Brownian motion (cf. Bertoin [4]). One of our motivations is that such a representation of fragmentation processes by excursion-type functions induces a particular order on the fragments which is closely related to the additivity of the coalescent kernel. We identify the fragmentation processes obtained this way as a mixing of time-reversed extremal additive coalescents by analogy with the work of Aldous and Pitman [2], and we make its semigroup explicit.

Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 14, 33 pp.

Dates
Accepted: 30 June 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097644

Digital Object Identifier
doi:10.1214/EJP.v6-87

Mathematical Reviews number (MathSciNet)
MR1844511

Zentralblatt MATH identifier
0974.60054

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G51: Processes with independent increments; Lévy processes

Keywords
Additivecoalescent fragmentation Lévy processes processes with exchangeableincrements

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Miermont, Grégory. Ordered Additive Coalescent and Fragmentations Associated to Lévy Processes with No Positive Jumps. Electron. J. Probab. 6 (2001), paper no. 14, 33 pp. doi:10.1214/EJP.v6-87. https://projecteuclid.org/euclid.ejp/1461097644


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