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2024 Alpha-stable branching and beta-frequency processes, beyond the IID assumption
Adrián González Casanova, Imanol Nuñez, José Luis Pérez
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Electron. Commun. Probab. 29: 1-12 (2024). DOI: 10.1214/23-ECP570


Birkner et al. obtained necessary and sufficient conditions for the frequency between two independent and identically distributed continuous-state branching processes time-changed by a functional of the total mass process to be a Markov process. Foucart et al. extended this result to continuous-state branching processes with immigration. We generalize these results by dropping the independent and identically distributed assumption. Our result clarifies under which conditions a multi-type Λ-coalescent can be constructed from a multi-type branching process by a time change using the total mass. Finally, we address a problem formulated by Griffiths, by clarifying the relation between 2-type α-stable continuous-state branching processes and 2-type β-Fleming–Viot processes with mutation and selection.


We want to thank the anonymous referee for the careful reading, constructive comments and suggestions, which significantly improved the presentation and the readability of the paper.


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Adrián González Casanova. Imanol Nuñez. José Luis Pérez. "Alpha-stable branching and beta-frequency processes, beyond the IID assumption." Electron. Commun. Probab. 29 1 - 12, 2024.


Received: 10 March 2023; Accepted: 15 December 2023; Published: 2024
First available in Project Euclid: 26 February 2024

Digital Object Identifier: 10.1214/23-ECP570

Primary: 60G52 , 60J80 , 60J90

Keywords: generators , immigration , multi-type continuous-state branching process , random time-change

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