Abstract
We derive the probability generating function for the general Bellman—Harris age dependent branching process with immigration emphasizing the role of immigration parameters. The solution requires solving a single scalar-valued integral equation, namely the usual Bellman—Harris equation. Our results are applied to three particular examples. We derive the equations for the immigration of particles governed by a Bellman—Harris process into a second Bellman—Harris process. In the second example we study Poisson immigration of particles into a time continuous Markov branching process. In the third, we derive the equations for a one-time immigration into a Bellman—Harris process.
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