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2001 Ordered Additive Coalescent and Fragmentations Associated to Lévy Processes with No Positive Jumps
Grégory Miermont
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Electron. J. Probab. 6: 1-33 (2001). DOI: 10.1214/EJP.v6-87

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.

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Grégory Miermont. "Ordered Additive Coalescent and Fragmentations Associated to Lévy Processes with No Positive Jumps." Electron. J. Probab. 6 1 - 33, 2001. https://doi.org/10.1214/EJP.v6-87

Information

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

zbMATH: 0974.60054
MathSciNet: MR1844511
Digital Object Identifier: 10.1214/EJP.v6-87

Subjects:
Primary: 60J25
Secondary: 60G51

Keywords: Additivecoalescent , fragmentation , Lévy processes , processes with exchangeableincrements

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