Year: 2023
Type: preprint
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 $Λ$-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.
Source: arXiv (Cornell University)
Authors: Casanova, Adrián González, Nuñez, Imanol, Pérez, J. -L.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4323927439