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Critical Galton–Watson processes by decreasing state-dependent immigration

Published online by Cambridge University Press:  14 July 2016

K. V. Mitov  and
N. M. Yanev
K. V. Mitov*
Affiliation:
Institute of Mathematics, Sofia
N. M. Yanev*
Affiliation:
Institute of Mathematics, Sofia
*
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P.O. Box 373, Bulgaria.
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P.O. Box 373, Bulgaria.
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Abstract

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.

Keywords

ASYMPTOTIC BEHAVIOURPROBABILITY FOR NON-EXTINCTIONMOMENTSLIMIT DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 22 - 39
Copyright
Copyright © Applied Probability Trust 1984 

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References

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