Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

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.
Complete list of metadata

Cited literature [23 references]  Display  Hide  Download
Contributor : Jean-Jil Duchamps Connect in order to contact the contributor
Submitted on : Tuesday, July 17, 2018 - 6:19:08 PM
Last modification on : Friday, August 5, 2022 - 3:00:05 PM
Long-term archiving on: : Thursday, October 18, 2018 - 4:02:23 PM


Files produced by the author(s)


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


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



Record views


Files downloads