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An asymptotic result for a subcritical branching process with immigration

Published online by Cambridge University Press:  17 April 2009

A. G. Pakes
Affiliation:
Monash University, Clayton, Victoria.
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Abstract

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Under weak hypotheses, the geometric ergodicity of the states of a subcritical branching process with immigration is demonstrated by obtaining an asymptotic representation of the transition probabilities.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Heathcote, C.R., “A branching process allowing immigration”, J. Roy. Statist. Soc. Ser. B 27 (1965), 138–143.Google Scholar
[2]Heathcote, C.R., “Corrections and comments on the paper ‘A branching process allowing immigration’”, J. Roy. Statist. Soc. Ser. B 28 (1966), 213217.Google Scholar
[3]Heathcote, C.R., Seneta, E. and Vere-Jones, D., “A refinement of two theorems in the theory of branching processes”, (Russian summary), Teor. Verojatnost. i Primenen. 12 (1967), 341346.Google Scholar
[4]Korevaar, J., van Aardenne-Ehrenfest, T. and de Bruijn, N., “A note on slowly oscillating functions”, Nieuw Arch. Wisk. (2) 23 (1949), 7786.Google Scholar
[5]Pakes, A.G., “Branching processes with immigration”, submitted to J. Roy. Statist. Soc.Google Scholar
[6]Seneta, E., “Functional equations and the Galton-Watson process”, Advances Appl. Prob. 1 (1969), 142.Google Scholar