2023/03/09 by Casanova, Adrián González, Nuñez, Imanol, Pérez, J. -L.
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2303.05477
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.