Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Ordered additive coalescents and additive coalescents associated to LÚvy processes with no positive jumps


Code(s) de Classification MSC:

RÚsumÚ: We study here the fragmentation processes that can be derived from L\'evy 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.

Mots ClÚs: Additive coalescent ; fragmentation ; LÚvy processes ; processes with exchangeable increments

Date: 2001-06-07

Prépublication numéro: PMA-664

Postscript file : PMA-664.ps