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Critical Galton–Watson processes by decreasing state-dependent immigration
K. V. Mitov, N. M. Yanev
Journal:

Journal of Applied Probability / Volume 21 / Issue 1 / March 1984

Published online by Cambridge University Press:

14 July 2016, pp. 22-39

Print publication:

March 1984
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This paper deals with the Foster–Pakes model for Galton–Watson branching processes allowing immigration whenever the number of particles is 0. In the critical case we investigate the asymptotic behaviour of the probability of non-extinction, of the expectation and of the variance, and obtain different types of limit theorems depending on the temporally-decreasing sizes of the immigrants.

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Critical Galton–Watson processes by decreasing state-dependent immigration