Electronic Journal of Probability

Growth-fragmentation processes and bifurcators

Quan Shi

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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 $.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 15, 25 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

growth-fragmentation Lévy process self-similarity

Creative Commons Attribution 4.0 International License.


Shi, Quan. Growth-fragmentation processes and bifurcators. Electron. J. Probab. 22 (2017), paper no. 15, 25 pp. doi:10.1214/17-EJP26. https://projecteuclid.org/euclid.ejp/1487127643

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