Fragmentations with self-similar branching speeds

Abstract : We consider fragmentation processes with values in the space of marked partitions of 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 Lévy-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.
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https://hal.sorbonne-universite.fr/hal-02179793
Contributor : Jean-Jil Duchamps <>
Submitted on : Thursday, July 11, 2019 - 10:56:25 AM
Last modification on : Friday, December 13, 2019 - 10:36:02 AM

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  • HAL Id : hal-02179793, version 1
  • ARXIV : 1907.04712

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Jean-Jil Duchamps. Fragmentations with self-similar branching speeds. 2019. ⟨hal-02179793⟩

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