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Homogeneous fragmentation processes. (English) Zbl 0992.60076
The author introduces a new Markovian process valued in the space of partitions of N, which describes the continuous random splitting of a given initial mass. This process can be viewed as a “marked” continuous state branching process. His main result is a Lévy-Itô representation, which decomposes the infinitesimal fragmentation into an erosion and a sudden dislocation. Asymptotic frequencies of blocks are also studied, with links to the theory of subordinators.

MSC:
60J25 Continuous-time Markov processes on general state spaces
60G09 Exchangeability for stochastic processes
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