Fragmentations with self-similar branching speeds
| Autor: | Duchamps, Jean-Jil |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider fragmentation processes with values in the space of marked partitions of $\mathbb{N}$, i.e. partitions where each block is decorated with a nonnegative real number. Assuming that the marks on distinct blocks evolve as independent positive self-similar Markov processes and determine the speed at which their blocks fragment, we get a natural generalization of the self-similar fragmentations of Bertoin (2002). Our main result is the characterization of these generalized fragmentation processes: a L\'evy-Khinchin representation is obtained, using techniques from positive self-similar Markov processes and from classical fragmentation processes. We then give sufficient conditions for their absorption in finite time to a frozen state, and for the genealogical tree of the process to have finite total length. Comment: 38 pages |
| Databáze: | arXiv |
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