Electronic Journal of Probability

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

Grégory Miermont

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Additivecoalescent fragmentation Lévy processes processes with exchangeableincrements

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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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