Alpha-stable branching and beta-Frequency processes, beyond the IID assumption
Abstract
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 -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 -stable continuous-state branching processes and 2-type -Fleming--Viot processes with mutation and selection.
Cite
@article{arxiv.2303.05477,
title = {Alpha-stable branching and beta-Frequency processes, beyond the IID assumption},
author = {Adrián González Casanova and Imanol Nuñez and J. -L. Pérez},
journal= {arXiv preprint arXiv:2303.05477},
year = {2023}
}