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.
Citation
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
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