%0 Generic %1 caballero2020ratio %A Caballero, María Emilia %A Casanova, Adrián González %A Pérez, José-Luis %D 2020 %K Wright-Fisher_diffusion branching_processes lambda_coalescent %T The ratio of two general continuous-state branching processes with immigration, and its relation to coalescent theory %U http://arxiv.org/abs/2010.00742 %X We study the ratio of two different continuous-state branching processes with immigration whose total mass is forced to be constant at a dense set of times. These lead to the definition of the $Łambda$- asymmetric frequency process ($Łambda$-AFP) as a solution of to an SDE. We prove that this SDE has a unique strong solution which is a Feller process. We also calculate a large population limit when the mass tends to infinity and study the fluctuations of the process around its deterministic limit. Furthermore, we find conditions for the $Łambda$-AFP to have a moment dual. The dual can be interpreted in terms of selection, (coordinated) mutation, pairwise branching (efficiency), coalescence, and a novel component that comes from the asymmetry between the reproduction mechanisms. A pair of equally distributed continuous-state branching processes has an associated $Łambda$-AFP whose dual is a $Łambda$-coalescent. The map that sends each continuous-state branching process to its associated $Łambda$-coalescent (according to the former procedure) is a homeomorphism between metric spaces.

@misc{caballero2020ratio, abstract = {We study the ratio of two different continuous-state branching processes with immigration whose total mass is forced to be constant at a dense set of times. These lead to the definition of the $\Lambda$- asymmetric frequency process ($\Lambda$-AFP) as a solution of to an SDE. We prove that this SDE has a unique strong solution which is a Feller process. We also calculate a large population limit when the mass tends to infinity and study the fluctuations of the process around its deterministic limit. Furthermore, we find conditions for the $\Lambda$-AFP to have a moment dual. The dual can be interpreted in terms of selection, (coordinated) mutation, pairwise branching (efficiency), coalescence, and a novel component that comes from the asymmetry between the reproduction mechanisms. A pair of equally distributed continuous-state branching processes has an associated $\Lambda$-AFP whose dual is a $\Lambda$-coalescent. The map that sends each continuous-state branching process to its associated $\Lambda$-coalescent (according to the former procedure) is a homeomorphism between metric spaces.}, added-at = {2021-06-29T18:52:30.000+0200}, author = {Caballero, María Emilia and Casanova, Adrián González and Pérez, José-Luis}, biburl = {https://www.bibsonomy.org/bibtex/2e818bb99324d66c96429544e11f695cd/peter.ralph}, interhash = {05aed498c7e57af4d2c276ad5b205340}, intrahash = {e818bb99324d66c96429544e11f695cd}, keywords = {Wright-Fisher_diffusion branching_processes lambda_coalescent}, note = {cite arxiv:2010.00742}, timestamp = {2021-06-29T18:52:30.000+0200}, title = {The ratio of two general continuous-state branching processes with immigration, and its relation to coalescent theory}, url = {http://arxiv.org/abs/2010.00742}, year = 2020 }