Electronic Journal of Probability

Growth-fragmentation processes and bifurcators

Quan Shi

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1487127643

Digital Object Identifier
doi:10.1214/17-EJP26

Mathematical Reviews number (MathSciNet)
MR3622885

Zentralblatt MATH identifier
1357.60052

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

Keywords
growth-fragmentation Lévy process self-similarity

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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