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Trees within trees II: Nested Fragmentations

Abstract : Similarly as in (Blancas et al. 2018) where nested coalescent processes are studied, we generalize the definition of partition-valued homogeneous Markov fragmentation processes to the setting of nested partitions, i.e. pairs of partitions $(\zeta,\xi)$ where $\zeta$ is finer than $\xi$. As in the classical univariate setting, under exchangeability and branching assumptions, we characterize the jump measure of nested fragmentation processes, in terms of erosion coefficients and dislocation measures. Among the possible jumps of a nested fragmentation , three forms of erosion and two forms of dislocation are identified – one of which being specific to the nested setting and relating to a bivariate paintbox process.
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https://hal.archives-ouvertes.fr/hal-01842036
Contributor : Jean-Jil Duchamps <>
Submitted on : Tuesday, July 17, 2018 - 6:19:08 PM
Last modification on : Friday, April 10, 2020 - 5:27:02 PM
Document(s) archivé(s) le : Thursday, October 18, 2018 - 4:02:23 PM

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  • HAL Id : hal-01842036, version 1
  • ARXIV : 1807.05951

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Jean-Jil Duchamps. Trees within trees II: Nested Fragmentations. 2018. ⟨hal-01842036⟩

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