A branching process with a state dependent immigration component

Consider the well known Galton-Watson branching process (Harris (1963)) in which individuals reproduce independently of each other and have probability a j (j = 0, 1, · · ·) of giving rise to j individuals in the next generation. In recent years some attention has been given to the branching process in which there is an independent immigration component at each generation, b j (j = 0, 1, · · ·) being the probability of j immigrants entering each generation. For a review of this work see Seneta (1969), and Pakes (1971 a, b and c) for further results.

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