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On branching processes allowing immigration

Published online by Cambridge University Press:  14 July 2016

Y. S. Yang
Y. S. Yang*
Affiliation:
Nanyang University, Singapore
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Abstract

Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.

Keywords

CONTINUOUS TIME MARKOV CHAINSBRANCHING PROCESSES ALLOWING IMMIGRATIONINVARIANT MEASURESPOSITIVE RECURRENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 24 - 31
Copyright
Copyright © Applied Probability Trust 1972 

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References

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