Open Access
2017 Growth-fragmentation processes and bifurcators
Quan Shi
Electron. J. Probab. 22: 1-25 (2017). DOI: 10.1214/17-EJP26


Markovian growth-fragmentation processes introduced by Bertoin model a system of growing and splitting cells in which the size of a typical cell evolves as a Markov process $X$ without positive jumps. We find that two growth-fragmentations associated respectively with two processes $X$ and $Y$ (with different laws) may have the same distribution, if $(X,Y)$ is a bifurcator, roughly speaking, which means that they coincide up to a bifurcation time and then evolve independently. Using this criterion, we deduce that the law of a self-similar growth-fragmentation is determined by its index of self-similarity and a cumulant function $\kappa $.


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Quan Shi. "Growth-fragmentation processes and bifurcators." Electron. J. Probab. 22 1 - 25, 2017.


Received: 28 March 2016; Accepted: 10 January 2017; Published: 2017
First available in Project Euclid: 15 February 2017

zbMATH: 1357.60052
MathSciNet: MR3622885
Digital Object Identifier: 10.1214/17-EJP26

Primary: 60G51 , 60J80

Keywords: Growth-fragmentation , Lévy process , self-similarity

Vol.22 • 2017
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