Skip to Main content Skip to Navigation
Theses

Some Aspects of Growth-Fragmentation

Abstract : This thesis treats stochastic aspects of fragmentation processes when growth and/or immigration of particles are incorporated as a compensating phenomenon. In a first part, we study the asymptotic behavior of self-similar growth-fragmentation processes, extending the results related to pure fragmentations. In a second part, we prove that self-similar growth-fragmentations arise as scaling limits of truncated Markov branching processes and we provide a rather general criterion. This bolsters the conviction that growth-fragmentations appear in many discrete Markovian structures, as already observed in random planar geometry. Lastly, we study a growth-fragmentation with immigration equation. In particular, we investigate the asymptotic behavior of the solution by relating it to a stochastic particle system in which immigrate copies of a certain growth-fragmentation process.
Document type :
Theses
Complete list of metadatas

Cited literature [113 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02441561
Contributor : Benjamin Dadoun <>
Submitted on : Wednesday, January 15, 2020 - 9:39:57 PM
Last modification on : Tuesday, January 21, 2020 - 1:03:48 AM
Long-term archiving on: : Thursday, April 16, 2020 - 5:37:24 PM

File

thesis_with_titlepage.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License

Identifiers

  • HAL Id : tel-02441561, version 1

Collections

Citation

Benjamin Dadoun. Some Aspects of Growth-Fragmentation. Probability [math.PR]. University of Zurich, 2019. English. ⟨tel-02441561⟩

Share

Metrics

Record views

49

Files downloads

94