A construction that extends Gillespie's sequential-sampling ('culling') transformation to the multitype setting: an autonomous multitype frequency process built from independent multitype CSBPs is shown to be in moment duality with the block-counting process of a multitype Lambda-coalescent, yielding a homeomorphism between the parameter spaces of multitype CSBPs and multitype Lambda-coalescents. The resulting Gillespie-multitype-Lambda-coalescent is identified with the Johnston-Kyprianou-Rogers multitype Lambda-coalescent (diverging from the Pitman-sense definition, unlike in one dimension), with forward-in-time multitype sequentially sampled processes introduced as moment duals.
This probability paper (math.PR, MSC 60J90/60J80) builds new connections between multitype Lambda-coalescents and multitype continuous-state branching processes (CSBPs). In one dimension, Caballero e…