Continuous-time multitype branching processes conditioned on very late extinction
Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob -transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.