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Further results on the critical Galton-Watson process with immigration

Published online by Cambridge University Press:  09 April 2009

A. G. Pakes
A. G. Pakes
Affiliation:
Department of Mathematics Monash UniversityMelbourne, Australia
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Consider a Galton-Watson process in which each individual reproduces independently of all others and has probability aj (j = 0, 1, …) of giving rise to j progeny in the following generation, and in which there is an independent immigration component where bj, (j = 0, 1, …) is the probability that j individuals enter the population at each generation. Defining Xn (n = 0, 1, …) to be the population size at the n- th generation, it is known that {Xn} defines a Markov chain on the non-negative integers.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 277 - 290
Copyright
Copyright © Australian Mathematical Society 1972

References

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