Changing the branching mechanism of a continuous state branching process using immigration
Romain Abraham, Jean-François Delmas (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition...